Elwyn Berlekamp - Combinatorial Game Theory  
   Elwyn's research in the field, including several papers.
   http://math.berkeley.edu/~berlek/cgt/index.html

Aviezri Fraenkel  
   A comprehensive bibliography on combinatorial games; several papers about combinatorial games; and information about where to publish such results.
   http://www.wisdom.weizmann.ac.il/~fraenkel

David Eppstein - Combinatorial Game Theory  
   Many up-to-date links, and a short introduction.
   http://www.ics.uci.edu/~eppstein/cgt/

Jeff Erickson - Mathematical Games, Toys, and Puzzles  
   Links to several game theorists and actual games, plus a brief introduction. Also a couple of papers on game theory, about Toads and Frogs and Sowing Games.
   http://compgeom.cs.uiuc.edu/~jeffe/mathgames.html

Games that interest John Conway  
   Clever Games for Clever People, from the book On Numbers and Games.
   http://www.cs.uidaho.edu/~casey931/conway/games.html

Dice Theorem  
   How many ways are there of throwing n indistinguishable dice each with m faces?
   http://www.hermetic.ch/misc/dice/dice1.htm

Erik Demaine's Combinatorial Games  
   Research on pushing blocks, Clickomania, Phutball, and sliding coins. Survey paper on algorithmic combinatorial game theory.
   http://theory.lcs.mit.edu/~edemaine/games/