A widely-distributed press release about the Hubble Deep Field
observations, <URL:http://oposite.stsci.edu/pubinfo/PR/96/01.html>,
reported the discovery of a vast number of new galaxies.  The
existence of many galaxies too faint to be hitherto detected was no
surprise, and calculations of the number of galaxies in the observable
Universe and searches for how they change with cosmic time must always
allow for the ones we can't detect, through some combination of
intrinsic faintness and great distance. What was of great interest in
the Hubble Deep field (and similar) data was just how any faint
galaxies were detected and what their colors and forms are. Depending
on just what level of statistical error can be tolerated, catalogs of
galaxies in the Hubble Deep Field list about 3000. This field covers
an area of sky of only about 0.04 degrees on a side, meaning that we
would need 27,000,000 such patches to cover the whole sky.  Ignoring
such factors as absorption by dust in our own Galaxy, which make it
harder to see outside in some directions, the Hubble telescope is
capable of detecting about 80 billion galaxies (although not all of
these within the foreseeable future!).  In fact, there must be many
more than this, even within the observable Universe, since the most
common kind of galaxy in our own neighborhood is the faint dwarfs
which are difficult enough to see nearby, much less at large
cosmological distances. For example, in our own local group, there are
3 or 4 giant galaxies which would be detectable at a billion
light-years or more (Andromeda, the Milky Way, the Pinwheel in
Triangulum, and maybe the Large Magellanic Cloud). However, there are
at least another 20 faint members, which would be difficult to find at
100 million light-years, much less the billions of light years to
which the brightest galaxies can be seen.