There are vast numbers of published neural network applications. If you
don't find something from your field of interest below, try a web search.
Here are some useful search engines:
http://www.google.com/
http://search.yahoo.com/
http://www.altavista.com/
http://www.deja.com/

General
-------

 o The Pacific Northwest National Laboratory: 
   http://www.emsl.pnl.gov:2080/proj/neuron/neural/ including a list of
   commercial applications at 
   http://www.emsl.pnl.gov:2080/proj/neuron/neural/products/ 
 o The Stimulation Initiative for European Neural Applications: 
   http://www.mbfys.kun.nl/snn/siena/cases/ 
 o The DTI NeuroComputing Web's Applications Portfolio: 
   http://www.globalweb.co.uk/nctt/portfolo/ 
 o The Applications Corner, NeuroDimension, Inc.: 
   http://www.nd.com/appcornr/purpose.htm 
 o The BioComp Systems, Inc. Solutions page: http://www.bio-comp.com 
 o Chen, C.H., ed. (1996) Fuzzy Logic and Neural Network Handbook, NY:
   McGraw-Hill, ISBN 0-07-011189-8. 
 o The series Advances in Neural Information Processing Systems containing
   proceedings of the conference of the same name, published yearly by
   Morgan Kauffman starting in 1989 and by The MIT Press in 1995. 

Agriculture
-----------

 o P.H. Heinemann, Automated Grading of Produce: 
   http://server.age.psu.edu/dept/fac/Heinemann/phhdocs/visionres.html
 o Deck, S., C.T. Morrow, P.H. Heinemann, and H.J. Sommer, III. 1995.
   Comparison of a neural network and traditional classifier for machine
   vision inspection. Applied Engineering in Agriculture. 11(2):319-326. 
 o Tao, Y., P.H. Heinemann, Z. Varghese, C.T. Morrow, and H.J. Sommer III.
   1995. Machine vision for color inspection of potatoes and apples.
   Transactions of the American Society of Agricultural Engineers.
   38(5):1555-1561. 

Automotive
----------

 o "No Hands Across America Journal" - steering a car: 
   http://cart.frc.ri.cmu.edu/users/hpm/project.archive/reference.file/Journal.html
   Photos: 
   http://www.techfak.uni-bielefeld.de/ags/ti/personen/zhang/seminar/intelligente-autos/tour.html

Chemistry
---------

 o PNNL, General Applications of Neural Networks in Chemistry and Chemical
   Engineering: 
   http://www.emsl.pnl.gov:2080/proj/neuron/neural/bib/chemistry.html. 
 o Prof. Dr. Johann Gasteiger, Neural Networks and Genetic Algorithms in
   Chemistry: 
   http://www2.ccc.uni-erlangen.de/publications/publ_topics/publ_topics-12.html
 o Roy Goodacre, pyrolysis mass spectrometry: 
   http://gepasi.dbs.aber.ac.uk/roy/pymshome.htm and Fourier transform
   infrared (FT-IR) spectroscopy: 
   http://gepasi.dbs.aber.ac.uk/roy/ftir/ftirhome.htm contain applications
   of a variety of NNs as well as PLS (partial least squares) and other
   statistical methods. 
 o Situs, a program package for the docking of protein crystal structures to
   single-molecule, low-resolution maps from electron microscopy or small
   angle X-ray scattering: http://chemcca10.ucsd.edu/~situs/ 
 o An on-line application of a Kohonen network with a 2-dimensional output
   layer for prediction of protein secondary structure percentages from UV
   circular dichroism spectra: http://www.embl-heidelberg.de/~andrade/k2d/. 

Criminology
-----------

 o Computer Aided Tracking and Characterization of Homicides and Sexual
   Assaults (CATCH): 
   http://lancair.emsl.pnl.gov:2080/proj/neuron/papers/kangas.spie99.abs.html

Face recognition
----------------

 o Face Recognition Home Page: http://www.cs.rug.nl/~peterkr/FACE/face.html 
 o Konen, W., "Neural information processing in real-world face-recognition
   applications," 
   http://www.computer.muni.cz/pubs/expert/1996/trends/x4004/konen.htm 
 o Jiang, Q., "Principal Component Analysis and Neural Network Based Face
   Recognition," http://people.cs.uchicago.edu/~qingj/ThesisHtml/ 
 o Lawrence, S., Giles, C.L., Tsoi, A.C., Back, A.D. (1997), "Face
   Recognition: A Convolutional Neural Network Approach," IEEE Transactions
   on Neural Networks, 8, 98-113, 
   http://www.neci.nec.com/~lawrence/papers/face-tnn97/latex.html 

Finance and economics
---------------------

 o Athanasios Episcopos, References on Neural Net Applications to Finance
   and Economics: http://www.compulink.gr/users/episcopo/neurofin.html 
 o Franco Busetti, Heuristics and artificial intelligence in finance and
   investment: http://www.geocities.com/francorbusetti/ 
 o Trippi, R.R. & Turban, E. (1993), Neural Networks in Finance and
   Investing, Chicago: Probus. 
 o Zirilli, J.S. (1996), Financial Prediction Using Neural Networks,
   International Thomson Publishing, ISBN 1850322341, 
   http://www6.bcity.com/mjfutures/ 
 o Andreas S. Weigend, Yaser Abu-Mostafa, A. Paul N. Refenes (eds.) (1997) 
   Decision Technologies for Financial Engineering: Proceedings of the Fourth
   International Conference on Neural Networks in the Capital Markets (Nncm
   '96) Publisher: World Scientific Publishing Company, ISBN: 9810231245 

Games, sports, gambling
-----------------------

 o General:

   Jay Scott, Machine Learning in Games: 
   http://satirist.org/learn-game/index.html

   METAGAME Game-Playing Workbench: 
   ftp://ftp.cl.cam.ac.uk/users/bdp/

   R.S. Sutton, "Learning to predict by the methods of temporal
   differences", Machine Learning 3, p. 9-44 (1988). 

   David E. Moriarty and Risto Miikkulainen (1994). "Evolving Neural
   Networks to Focus Minimax Search," In Proceedings of Twelfth National
   Conference on Artificial Intelligence (AAAI-94, Seattle, WA), 1371-1377.
   Cambridge, MA: MIT Press, 
   http://www.cs.utexas.edu/users/nn/pages/publications/neuro-evolution.html

   Games World '99 at http://gamesworld99.free.fr/menuframe.htm

 o Backgammon:

   G. Tesauro and T.J. Sejnowski (1989), "A Parallel Network that learns to
   play Backgammon," Artificial Intelligence, vol 39, pp. 357-390. 

   G. Tesauro and T.J. Sejnowski (1990), "Neurogammon: A Neural Network
   Backgammon Program," IJCNN Proceedings, vol 3, pp. 33-39, 1990. 

   G. Tesauro (1995), "Temporal Difference Learning and TD-Gammon,"
   Communications of the ACM, 38, 58-68, 
   http://www.research.ibm.com/massive/tdl.html 

   Pollack, J.P. and Blair, A.D. (1997), "Co-Evolution in the Successful
   Learning of Backgammon Strategy," Brandeis University Computer Science
   Technical Report CS-97-193, 
   http://www.demo.cs.brandeis.edu/papers/long.html#hcgam97

 o Bridge:

   METAGAME: ftp://ftp.cl.cam.ac.uk/users/bdp/

   He Yo, Zhen Xianjun, Ye Yizheng, Li Zhongrong (19??), "Knowledge
   acquisition and reasoning based on neural networks - the research of a
   bridge bidding system," INNC '90, Paris, vol 1, pp. 416-423. 

   M. Kohle and F. Schonbauer (19??), "Experience gained with a neural
   network that learns to play bridge," Proc. of the 5th Austrian Artificial
   Intelligence meeting, pp. 224-229. 

 o Checkers/Draughts: 

   Mark Lynch (1997), "NeuroDraughts: an application of temporal difference
   learning to draughts," 
   http://www.ai.univie.ac.at/~juffi/lig/Papers/lynch-thesis.ps.gz Software
   available at 
   http://satirist.org/learn-game/archive/NeuroDraughts-1.00.zip

   K. Chellapilla and D. B. Fogel, "Co-Evolving Checkers Playing Programs
   using Only Win, Lose, or Draw," SPIE's AeroSense'99: Applications and
   Science of Computational Intelligence II, Apr. 5-9, 1999, Orlando,
   Florida, USA, http://vision.ucsd.edu/~kchellap/Publications.html 

   David Fogel (1999), Evolutionary Computation: Toward a New Philosophy
   of Machine Intelligence (2nd edition), IEEE, ISBN: 078035379X 

   David Fogel (2001), Blondie24: Playing at the Edge of AI, Morgan Kaufmann
   Publishers, ISBN: 1558607838
   According to the publisher, this is: 

   ... the first book to bring together the most advanced work in the
   general use of evolutionary computation for creative results. It is
   well suited for the general computer science audience. 

   Here's the story of a computer that taught itself to play checkers
   far better than its creators ever could. Blondie24 uses a program
   that emulates the basic principles of Darwin evolution to discover on
   its own how to excel at the game. Through this entertaining story,
   the book provides the reader some of the history of AI and explores
   its future. 

   Unlike Deep Blue, the celebrated chess machine that beat Garry
   Kasparov, the former world champion chess player, this evolutionary
   program didn't have access to other games played by human grand
   masters, or databases of moves for the endgame. It created its own
   means for evaluating the patterns of pieces that it experienced by
   evolving artificial neural networks--mathematical models that loosely
   describe how a brain works. 

See http://www.natural-selection.com/NSIPublicationsOnline.htm for a variety
of online papers by Fogel. 

Not NNs, but classic papers:

A.L. Samuel (1959), "Some studies in machine learning using the game of
checkers," IBM journal of Research and Development, vol 3, nr. 3, pp.
210-229. 

A.L. Samuel (1967), "Some studies in machine learning using the game of
checkers 2 - recent progress," IBM journal of Research and Development, vol
11, nr. 6, pp. 601-616. 

o Chess:

Sebastian Thrun, NeuroChess: 
http://satirist.org/learn-game/systems/neurochess.html

Luke Pellen, Octavius: http://home.seol.net.au/luke/octavius/

Louis Savain (AKA Nemesis), Animal, a spiking neural network that the author
hopes will learn to play a passable game of chess after he implements the
motivation mechanism: 
http://home1.gte.net/res02khr/AI/Temporal_Intelligence.htm

o Dog racing:

H. Chen, P. Buntin Rinde, L. She, S. Sutjahjo, C. Sommer, D. Neely (1994),
"Expert Prediction, Symbolic Learning, and Neural Networks: An Experiment on
Greyhound Racing," IEEE Expert, December 1994, 21-27, 
http://ai.bpa.arizona.edu/papers/dog93/dog93.html

o Football (Soccer):

Kuonen Diego, "Statistical Models for Knock-out Soccer Tournaments", 
http://dmawww.epfl.ch/~kuonen/CALCIO/ (not neural nets, but relevant)

o Go:

David Stoutamire (19??), "Machine Learning, Game Play, and Go," Center for
Automation and Intelligent Systems Research TR 91-128, Case Western Reserve
University. http://www.stoutamire.com/david/publications.html 

David Stoutamire (1991), Machine Learning Applied to Go, M.S. thesis, Case
Western Reserve University, ftp://ftp.cl.cam.ac.uk/users/bdp/ 

Schraudolph, N., Dayan, P., Sejnowski, T. (1994), "Temporal Difference
Learning of Position Evaluation in the Game of Go," In: Neural Information
Processing Systems 6, Morgan Kaufmann 1994, 
ftp://bsdserver.ucsf.edu/Go/comp/ 

P. Donnelly, P. Corr & D. Crookes (1994), "Evolving Go Playing Strategy in
Neural Networks", AISB Workshop on Evolutionary Computing, Leeds, England, 
ftp://www.joy.ne.jp/welcome/igs/Go/computer/egpsnn.ps.Z or 
ftp://ftp.cs.cuhk.hk/pub/neuro/GO/techreports/egpsnn.ps.Z 

Markus Enzenberger (1996), "The Integration of A Priori Knowledge into a Go
Playing Neural Network," 
http://www.cgl.ucsf.edu/go/Programs/neurogo-html/neurogo.html 

Norman Richards, David Moriarty, and Risto Miikkulainen (1998), "Evolving
Neural Networks to Play Go," Applied Intelligence, 8, 85-96, 
http://www.cs.utexas.edu/users/nn/pages/publications/neuro-evolution.html 

Dahl, F. A. (1999), "Honte, a Go-playing program using neural nets", 
http://www.ai.univie.ac.at/icml-99-ws-games/papers/dahl.ps.gz 

o Go-Moku:

Freisleben, B., "Teaching a Neural Network to Play GO-MOKU," in I.
Aleksander and J. Taylor, eds, Artificial Neural Networks 2, Proc. of
ICANN-92, Brighton UK, vol. 2, pp. 1659-1662, Elsevier Science Publishers,
1992 

Katz, W.T. and Pham, S.P. "Experience-Based Learning Experiments using
Go-moku", Proc. of the 1991 IEEE International Conference on Systems, Man,
and Cybernetics, 2: 1405-1410, October 1991. 

o Olympics:

E.M.Condon, B.L.Golden, E.A.Wasil (1999), "Predicting the success of nations
at the Summer Olympics using neural networks", Computers & Operations
Research, 26, 1243-1265. 

o Pong:

http:// www.engin.umd.umich.edu/~watta/MM/pong/pong5.html 

o Reversi/Othello:

David E. Moriarty and Risto Miikkulainen (1995). Discovering Complex Othello
Strategies through Evolutionary Neural Networks. Connection Science, 7,
195-209, 
http://www.cs.utexas.edu/users/nn/pages/publications/neuro-evolution.html 

Yoshioka, T., Ishii, S., and Ito, M., Strategy acquisition for the game
``Othello'' based on reinforcement learning, IEICE Transactions on
Information and Systems E82-D 12, 1618-1626, 1999, 
http://mimi.aist-nara.ac.jp/~taku-y/ 

o Tic-Tac-Toe/Noughts and Crosses:

Fogel, David Bb (1993), "Using evolutionary programming to construct neural
networks that are capable of playing tic-tac-toe," Intern. Conf. on Neural
Networks 1993, IEEE, San Francisco, CA, pp. 875-880. 

Richard S. Sutton and Andrew G. Barto (1998), Reinforcement Learning: An
Introduction The MIT Press, ISBN: 0262193981, 
http://www-anw.cs.umass.edu/~rich/book/the-book.html 

Yongzheng Zhang, Chen Teng, Sitan Wei (2000), "Game playing with
Evolutionary Strategies and Modular Neural Networks: Tic-Tac-Toe," 
http://www.cs.dal.ca/~mheywood/GAPproject/EvolvingGamePlay.html 

Rob Ellison, "Neural Os and Xs," 
http://www.catfood.demon.co.uk/beta/game.html (An online Javascript demo,
but you may not live long enough to teach the network to play a mediocre
game. I'm not sure what kind of network it uses, but maybe you can figure
that out if you read the source.) 

http://listserv.ac.il/~dvorkind/TicTacToe/main_doc.htm, Java classes by Tsvi
Dvorkind, using reinforcement learning. 

Industry
--------

 o PNNL, Neural Network Applications in Manufacturing: 
   http://www.emsl.pnl.gov:2080/proj/neuron/neural/bib/manufacturing.html. 
 o PNNL, Applications in the Electric Power Industry: 
   http://www.emsl.pnl.gov:2080/proj/neuron/neural/bib/power.html. 
 o PNNL, Process Control: 
   http://www.emsl.pnl.gov:2080/proj/neuron/neural/bib/process.html. 
 o Raoul Tawel, Ken Marko, and Lee Feldkamp (1998), "Custom VLSI ASIC for
   Automotive Applications with Recurrent Networks", 
   http://www.jpl.nasa.gov/releases/98/ijcnn98.pdf 
 o Otsuka, Y. et al. "Neural Networks and Pattern Recognition of Blast
   Furnace Operation Data" Kobelco Technology Review, Oct. 1992, 12 
 o Otsuka, Y. et al. "Applications of Neural Network to Iron and Steel
   Making Processes" 2. International Conference on Fuzzy Logic and Neural
   Networks, Iizuka, 1992 
 o Staib, W.E. "Neural Network Control System for Electric Arc Furnaces"
   M.P.T. International, 2/1995, 58-61 
 o Portmann, N. et al. "Application of Neural Networks in Rolling
   Automation" Iron and Steel Engineer, Feb. 1995, 33-36 
 o Gorni, A.A. (2000), "The modelling of hot rolling processes using neural
   networks: A bibliographical review", 
   http://www.geocities.com/SiliconValley/5978/neural_1998.html 
 o Murat, M. E., and Rudman, A. J., 1992, Automated first arrival picking: A
   neural network approach: Geophysical Prospecting, 40, 587-604. 

Materials science
-----------------

 o Phase Transformations Research Group (search for "neural"): 
   http://www.msm.cam.ac.uk/phase-trans/pubs/ptpuball.html 

Medicine
--------

 o PNNL, Applications in Medicine and Health: 
   http://www.emsl.pnl.gov:2080/proj/neuron/neural/bib/medicine.html. 

Music
-----

 o Mozer, M. C. (1994), "Neural network music composition by prediction:
   Exploring the benefits of psychophysical constraints and multiscale
   processing," Connection Science, 6, 247-280, 
   http://www.cs.colorado.edu/~mozer/papers/music.html. 
 o Griffith, N., and Todd, P.M., eds. (1999), Musical Networks: Parallel
   Distributed Perception and Performance, Cambridge, MA: The MIT Press,
   ISBN 0-262-07181-9. 

Robotics
--------

 o Institute of Robotics and System Dynamics: 
   http://www.robotic.dlr.de/LEARNING/ 
 o UC Berkeley Robotics and Intelligent Machines Lab: 
   http://robotics.eecs.berkeley.edu/ 
 o Perth Robotics and Automation Laboratory: 
   http://telerobot.mech.uwa.edu.au/ 
 o University of New Hampshire Robot Lab: 
   http://www.ece.unh.edu/robots/rbt_home.htm 

Weather forecasting and atmospheric science
-------------------------------------------

 o UBC Climate Prediction Group: 
   http://www.ocgy.ubc.ca/projects/clim.pred/index.html 
 o Artificial Intelligence Research In Environmental Science: 
   http://www.salinas.net/~jpeak/airies/airies.html 
 o MET-AI, an mailing list for meteorologists and AI researchers: 
   http://www.comp.vuw.ac.nz/Research/met-ai 
 o Caren Marzban, Ph.D., Research Scientist, National Severe Storms
   Laboratory: http://www.nhn.ou.edu/~marzban/ 
 o David Myers's references on NNs in atmospheric science: 
   http://terra.msrc.sunysb.edu/~dmyers/ai_refs 

Weird
-----

Zaknich, Anthony and Baker, Sue K. (1998), "A real-time system for the
characterisation of sheep feeding phases from acoustic signals of jaw
sounds," Australian Journal of Intelligent Information Processing Systems
(AJIIPS), Vol. 5, No. 2, Winter 1998. 

Abstract
This paper describes a four-channel real-time system for the detection and
measurement of sheep rumination and mastication time periods by the analysis
of jaw sounds transmitted through the skull. The system is implemented using
an 80486 personal computer, a proprietary data acquisition card (PC-126) and
a custom made variable gain preamplifier and bandpass filter module. Chewing
sounds are transduced and transmitted to the system using radio microphones
attached to the top of the sheep heads. The system's main functions are to
detect and estimate rumination and mastication time periods, to estimate the
number of chews during the rumination and mastication periods, and to
provide estimates of the number of boli in the rumination sequences and the
number of chews per bolus. The individual chews are identified using a
special energy threshold detector. The rumination and mastication time
periods are determined by neural network classifier using a combination of
time and frequency domain features extracted from successive 10 second
acoustic signal blocks.