Earlier, Mustangsal and I chatted a bit about favorite games for mental exercise and thought it would be a good forum topic where everyone could post a list of their favorite games of this genre regardless of whether they're Flash/Shockwave type or not. When I embarked on this post I was delighted to find a daily crossword puzzle at the bottom of this forum area, too!
Just good games that challenge how you figure out stuff. I'll kick off with my own list but it's subject to additions when I think of them. Unfortunately most of them are Flash games so I wish somebody somewhere would do up HTML versions of the same:
(sliding blocks type)
Aztec Mind
various slider puzzles
Miner Block
Sliding Blocks (this and the previous game are already on this site)
(hexagon type)
Virus Hex Options
Hexalot
Hexover
Hexagonator
(strategy puzzle type)
Parking Zone
Numbrix
Toy Match
Othello
Reversi
Mastermind
I'm not including Sudoku because increased difficulty involving several matched pairs diminishes analytic value of solving.
This list is just for starters--add to the list at will.