Information about past mathematicians is available from Trinity College, Dublin as well as St. Andrews, which also has pictures. More pictures are found at NYU. More math history is at Clark University, and another site specializes in women mathematicians.
The Mathematical Association of America, the American Mathematical Society, and the International Mathematical Union are all online. Another institution with extensive online math offerings is the Univ. of Tennessee, Knoxville. Mathematical software is available from the National Institute of Standards and Technology, SIAM, and the Netlib Repository; Penn. State has additional math software links. Commercial math resources include MathPro, Soft Warehouse (the makers of Derive), Wolfram Research (Mathematica), Springer-Verlag, and "Numerical Recipes in C".
Some interactive resources are Neil Sloane's On-Line Encyclopedia of Integer Sequences, searchable by numbers, authors and keywords; the CECM Inverse Symbolic Calculator, which given ".281718171541" will return "3 - e"; Pi-Search, which will see if your phone number occurs in the first million or so digits of pi, and the charming home page of Eve Anderssen, which will lead you to her pi trivia quiz.
Math journals which are more or less online include the Electronic Journal of Combinatorics, the The MathVISION technical journal, the Southwest Journal of Pure and Applied Mathematics, and the Journal of Graph Algorithms and Applications.
Some individuals have put together terrific math sites: Dave Rusin has collected and organized the gems from the noise and nonsense in sci.math; Kevin Brown has archived Usenet and email correspondence about problems that interest him, primarily in discrete math. John Baez produces a weekly essay on mathematical physics. Clifford Pickover offers computer art, virtual caverns, and information on his books. Henry Baker has extensive resources on Gaussian integers, quaternions, and the MIT AI Lab's famous HAKMEM. Other people with mathematics papers online include LISP inventor John McCarthy, algebraist Richard Botting, Miguel A. Lerma, complexity theorist Gregory Chaitin, and someone who calls himself "the Homeless Mathematician".
The best web site for geometry is the Geometry Forum homepage. Other geometry sites offer some very nice graphics polyhedra with model construction tips, information on adventitious angles, a course in fractal geometry, and sphere eversion.
The biggest number theory resource is the Number Theory web. On specific topics, there's David Moews' list of sociable numbers, information about Fermat's Last Theorem, elliptic curve point counting, and Mersenne primes. And, of course, my own pages on multiperfect numbers.
Everything you could possibly want to know about computing pi can be found at CECM, Mathsoft, or from Joerg Arndt. A less serious viewpoint can be found at the useless pi page. You can search for digit sequences in pi at Pi-Search, or take Eve Anderssen's pi trivia quiz. If your interests extend beyond pi, Steven Finch's Favorite Mathematical Constants include the famous and the obscure.
Competitions and problems:
The Middle and high school math competitions page at Stanford,
Mathpro's unsolved problem of the week,
the Math Olympiad in Poland.
Some algebra topics:
a lot of good stuff on forms,
a catalog of algebraic structures,
and John Pedersen's page on algebraic systems.
Other pointers, still unsorted:
More math info from WRI
Buser, Conway, Doyle, Semmler on "isosonic" drums
Images and movies of isospectral drums
Saturday Math School on the Net
Interactive Math Tutorial Software
Cutting sticks problem
``The Probability Web'', a collection of pages on probability
info on symbolic math packages (NL)
The Wavelet Digest
introductory papers on wavelets
The Erdos Number Project Home Page
Math-Net Links to the Mathematical World