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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.]
The Monty Hall Problem - A probability theory puzzle with solutions. [English and German.]
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.
The Puzzles of Oscar - Contains puzzles and games with 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 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.