Here are a few home pages of people working in combinatorics and related areas, together with reasons that one might like to visit them.
Peter Borwein has one of the fanciest home pages I know. It is also full of good things. It is definitely the place to go if you want to find out about problems and results to do with polynomials, particularly the effect on their behaviour of restricting their coefficients in various natural ways.
Bernard Chazelle has written a very interesting book on discrepancy. I particularly recommend Chapter 2 for a presentation of some of the ideas surrounding Wiles's proof of Fermat's last theorem (though the book needs them for a different problem). It is aimed at serious mathematicians, but gives plenty of motivation for concepts such as modular forms, Hecke operators etc. and does not assume very much background knowledge. A rare treat.
Fan Chung has many of her papers available online about topics such as random walks on graphs, discrete Laplacians, eigenvalues and so on. She also has some good links.
Vasek Chvátal is a very good starting point for exploring combinatorics on the internet.
Joshua Cooper has some nice results on his web page, including a detailed treatment of quasirandom permutations.
Marianna Csörnyei has a home page with preprints of her remarkable papers and an interesting selection of open problems.
Lance Fortnow has a home page with interesting papers on complexity, including one where he explains quantum computation in a "pure" way that doesn't require you to know quantum mechanics.
Ehud Friedgut has important results on sensitivity of Boolean functions, sharp thresholds and other topics.
Alan Frieze has many preprints available, on probabilistic combinatorics and computer science. They include interesting joint work with Ravi Kannan related to Szemerédi's regularity lemma.
Andrew Granville has papers available on many topics in number theory, usually with an analytic/combinatorial flavour. He also has useful links.
Ben Green has interesting papers in combinatorial number theory and a number of clear expositions of topics that most people make look hard. For example, his page is where I would suggest starting if you want to learn about sieve theory.
Mark Jerrum has a home page with many good papers and links on theoretical computer science and mixing rates of Markov chains.
Gil Kalai has proved beautiful results in several areas of combinatorics. His home page includes several downloadable papers.
Ravi Kannan is an expert on rapidly mixing Markov chains, amongst other topics, and has several papers available.
Yoshiharu Kohayakawa has many useful combinatorics links, and promises to add links to some of his own papers in due course.
Michael Krivelevich has proved several important results in combinatorics, and many of his papers are available online.
Izabella Laba has a page with a good description of the Kakeya problem, including a summary of the best known bounds. She promises to update it regularly.
László Lovász has many interesting papers available online, including survey papers about random walks on graphs, mixing times and so on.
Jiri Matousek has links to his fascinating papers and books (some not yet published) on combinatorial geometry.
If you suddenly need to know the 87,345th zero of the Riemann zeta function to 8 decimal places, then Andrew Odlyzko can help.
Steven Rudich has papers available in theoretical computer science, including `Natural Proofs' (joint with Razborov), which is a fascinating contribution to our understanding of the P=NP problem. (Click on `Research' to find them.)
Imre Ruzsa is incapable of proving anything uninteresting. A selection of his downloadable papers can be found here .
If you are short of mathematical reading matter, then Saharon Shelah's page should keep you busy for a while.
Neil Sloane's page has plenty of information and links to plenty more about sphere packings, codes, interesting sequences of integers etc.
Benny Sudakov has interesting papers available online on random and quasirandom graphs, and on other topics as well.
For more material on the Kakeya problem, as well as many other interesting questions, a visit to the incredible home page of Terence Tao is recommended.
Ilan Vardi has a page with plenty to explore.
Umesh Vazirani , from Berkeley, is interested in quantum computation, and has papers and course notes on the subject. His "Go With The Winners" paper is also very interesting, and suggests that evolutionary algorithms aren't as exciting as some people think.
Jacques Verstraete has an interesting list of research problems in combinatorics, some new, some old.
Avi Wigderson has many seminal papers on the complexity of Boolean functions and related areas.
Herb Wilf is an expert on generating functions. Amazingly, it is possible to download his entire book on the subject from his home page.
Peter Winkler has most of his recent papers in ps versions available online. These include papers on percolation and on Markov chains.
There are worse ways of being entertained than reading a few of the Opinions of Doron Zeilberger or visiting his home page .
The graph theory white pages have a list of many graph theorists, with links to many of their publications.
This page contains links to a selection of miscellaneous mathematical topics. It is worth a browse.
It can also be amusing to find out what's new in mathematics courtesy of the AMS.