1] J. V. Narlikar, Introduction to Cosmology.1983 Jones & Bartlett Publ.
For people with a solid background in physics and higher math, THE 
introductory text, IMHO, because it hits the balance between 
mathematical accuracy (tensor calculus and stuff) and intuitive
clarity/geometrical models very well for grad student level. Of course,
it has flaws but only noticeable by the Real Experts (TM) ...

2] Hawking: Brief History of Time 
Popular Science

3] Weinberg: First Three Minutes 
A very good book.  It's pretty old, but most of the information in it 
is still correct.

4] Timothy Ferris: Coming of Age in the Milky Way.
Popular Science.

5] Kolb and Turner: The Early Universe.
At a more advanced level, a standard reference.  As the title implies, 
K&T cover mostly the strange physics of very early times: it's heavy 
on the particle physics, and skimps on the astrophysics.  There's a 
primer on large-scale structure, which is the most active area of 
cosmological research, but it's really not all that good.

6] Peebles: Principles of Physical Cosmology.
Comprehensive, and on the whole it's quite a good book, but it's 
rather poorly organized.  I find myself jumping back and forth through
the book whenever I want to find anything.

7] "Black Holes and Warped Spacetime", by William J. Kaufmann, III.
This is a great, fairly thorough, though non-mathematical
description  of black holes and spacetime as it relates to
cosmology. I was impressed by how few mistakes Kaufmann makes in
simplifying, while most such books tend to sacrifice accuracy for
simplicity.

8] "Principles of Cosmology and Gravitation", Berry, M. V.
This is very well-written, and useful as an undergrad text.

9] Dennis Overbye: Lonely Hearts of the Cosmos
The unfinished history of converge on Hubble's constant is 
presented, from the perspective of competing astrophysics 
rival teams and institute, along with a lot of background on cosmology 
(a lot on inflation, for instance).  A good insight into the scientific
process.

10] The big bang / Joseph Silk.
I consider Silk's book an absolute must for those who want a quick run
at the current state of big bang cosmology and some of the recent
(1988)issues which have given so many of us lots of problems to solve.

10] Bubbles, voids, and bumps in time : the new cosmology / edited
by James Cornell.
This is quite a nice and relatively short read for some of the
pressing issues (as of 1987-88) in astrophysical cosmology.

11] Structure formation in the universe / T. Padmanabhan.
A no-nonsense book for those who want to calculate some problems
strictly related to the formation of structure in the universe.
The book even comes complete with problems at the end of each chapter.
A bad thing about this book is that there isn't any coverage on
clusters of galaxies and the one really big thing that annoys the
hell outta me is that the bibliography for *each* chapter is all
combined in one big bibliography towards the end of the book which
makes for lots of page flipping.

12] The large-scale structure of the universe / by P. J. E. Peebles.
This is a definitive book for anyone who desires an understanding of
the mathematics required to develop the theory for models of
large scale structure.  The essential techniques in the description
of how mass is able to cluster under gravity from a smooth early
universe are discussed.  While I find it dry in some places, there are
noteworthy sections (e.g. statistical tests, n-point correlation functions,
etc.).

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