CellFighter: Shareware game based around an extension of the game of life.
IBM Research: Ponder This: Monthly logic and math puzzles set by IBM researchers with solutions.
Jim Loy's Puzzle Page: Classic and original puzzles.
Kakuro-san: Providing graded Kakuro puzzles every day, plus old puzzles.
Leisure Ideas: Puzzles: Some mathematical puzzles with answers and/or a hint.
Mathematical Jigsaw Puzzles: Information on polyominos and square puzzles.
Monty Hall Game: JavaScript example of the Monty Hall Game. This game demonstrates the real (empirical) affect of statistics. [Does not display correctly in all browsers.]
Perplexus: A forum and collection of brain teasers, logic problems, math problems, paradoxes, science games, probability, riddles, and geometric shapes. The puzzles are searchable and categorized, most have solutions.
Quick Logic Puzzles: Use the clues provided to deduce the correct sequence of numbers in the hidden code.
TechInterview: Answers to technical interview questions, programming problems, and brain teasers.
The Monty Hall Problem: A probability theory puzzle with solutions. [English and German.]
The Puzzles of Oscar: Contains puzzles and games with solutions.
The Truth Tree's Math and Logic Board: Collection of math and logic puzzles ranging in levels of difficulty.
Two Envelope Paradox - Solution: Claims that the two envelope paradox comes from the incorrect use of probabilities.
WU Forums: Discussion board hosted at Berkeley with talk about a variety of solved and unsolved brain teasers.