Okay, so this isn't about all kinds of puzzles---it's really about mathematical puzzles, and there's a focus on puzzles that I like (particularly wooden polyhedral dissection puzzles).
Interlocking Puzzle Index (PuzzleWorld)
Ed Pegg's math puzzles
The Puzzling World of Polyhedral Dissections by Stewart Coffin
Amazing Puzzles to look at:
Wayne Daniel's Puzzles
Lee Krasnow's Puzzles
Michael Toulouzas' Puzzles
George Hart's Puzzles
Places to Play with Puzzles:
clickmazes (hosts a collection of Oskar VanDeventer puzzles)
Places to Buy Interesting Puzzles and/or Really Nice Puzzles:
Binary Arts (now called ThinkFun)
Bart Buie's Stewart Coffin Puzzles
Cubic Dissection (also has forums and a gallery)
Tessellations and MathArtFun
Bill Cutler Puzzles, Inc.
Mr. Puzzle Australia
Puzzle Master Inc.