Artnet
www.artnet.com
Artnet is one of the most established online art galleries I have seen. And in fact it does proclaim to be the largest of its kind. Artnet features Galleries and Artists by name and by genre. You can browse each artists work or you can search for a particular artist.
If you are a serious art collector Artnet is definately the place to come, they have work by famous artists such as Frank Auerbach, Vincent Van Gogh, Oskar Kokoschka and in fact almost any artist you can think of.