Check out the Inverse Symbolic Calculator from Simon Fraser University in British Columbia. If you have a number which looks familiar, but you can't remember where it came from, the ISC will try to give you its mathematical pedigree! (It's not a reverse phone book)
This one can be done just using E-mail! It's from a fairly mad mathematician at Bell Labs named Neil Sloane. Jump over to Sloane's Instructions to start. Basically, if you know the first few positive integers in a sequence, Sloane's machine can tell you if they're famous!
The AMSG is a "fractal-free" zone. For those who like pretty and mathematically interesting pictures we highly recommend --- the KnotPlot. With a little practice and a very good connection you can even make your own!
Of course the Web is the Web, so you'll want to do your own Math Surfing - here's a good quality starting place which seems to be lurking at Florida State - OTHER MATH SITES.
Try this link (Ooh, that's bad HTML!) if you want to experiment with some enumerative and graphical combinatorial objects. Frank Ruskey's ratings of his own links are about right!
This is called the Geometry Forum. It's been around a while so it's accumulated some (gasp!) not-so-mathematical content, but it might wind up your favorite!
This one, at the Geometry Center at the University of Minnesota, is a little more hard-core, but still can be fun.