The comprehensive index to on-line astronomical pictures and simulations is the NRAO Pretty Pictures page. Some of my favorites among the sites listed there are the following.
1. The Astronomy Picture of the Day, by Robert Nemiroff and Jerry Bonnell really is worth looking at every day. Its searchable archive is useful too.
2. Nice radio images of quasars and other active galaxies, mostly made with the Very Large Array (VLA), abound on the Web pages at the National Radio Astronomy Observatory (NRAO). I particularly like those in Dr. Alan Bridle's gallery.
3. Good places to find the best Hubble Space Telescope (HST) images are the SEDS Best of HST site, the Space Telescope Science Institute (STScI) Hubble NewsCenter, and the Hubble Heritage Project.
4. Lots of good images of supernovae can be found at Dave Bishop's site. This site is locally produced and maintained; Dave is one of the leaders of the Astronomy Section of the Rochester Academy of Sciences, the most sophisticated organization of amateur astronomers I've ever encountered.
5. The Anglo-Australian Observatory (AAO) is home to the all-time greatest astronomical photographer, David Malin. To gain a proper appreciation for Malin's work one must really see large-format high-quality prints of them (preferably made by Malin himself), but one can get started on the low-resolution copies of some of his best pictures at the AAO Web site.
Much more extensive on-line astronomy resources are available from the STScI's Astro Web and from pages linked to the American Astronomical Society (AAS) Home Page.