The Puzzle Toad at CMU has challenging puzzles.
William Wu's Puzzles Page at Berkeley has myriad puzzles with a discussion board.
Cut the Knot has dozens of high quality articles on mathematics, puzzles and games.
Puzzles by Erich Friedman has cute puzzles; he also maintains Math Magic, Erich's Packing Center and Ambigrams.
Archives of Ed Pegg Jr's Math Games in MAA make interesting reading.
Age of Puzzles is a nicely done website with classic puzzles, diagrams and references.
Sam Lloyd website: A few of his puzzles have tastefully been compiled at this website.
SOMA cube has dozens of SOMA cube configurations.
List of books by Martin Gardner.
Select puzzles for high school students: SNAP Math Fair.
Another small collection.
A nice collection of problems at mathproblems.info.
Another collection of puzzles.
Yet another collection by Tanya Khovanova.
Some problems by Mihai Patrascu.
Several ingenious puzzles at MathOveflow.Net.
Coin Puzzles: (a) Challenging Coin Puzzles by Terry Stickels, (b) Sliding Coin Puzzles and Games.
Prisoner and Hat Puzzles.
Surprises! Surprises! Surprises!.
MSRI Archives (puzzles in each newsletter).
Nice C Puzzles by Gowri Kumar.
Interesting articles on various problems.