If you're looking at post-1999, you can find plenty of creative, original puzzle games on
Kongregate's puzzle game section. Registration is optional, but if you want to record your scores and achievements, you should sign up. Plenty of other genres there too, like Action, Shooting, and RPG. Puzzle Quest: Challenge of the Warlords was on several consoles, and is fun. I used to go on 2 hour binges with that game on my DS while my laptop was down.
As with the pre-2000 puzzle games, I'd say Columns, Puyo Puyo (localized as Dr. Robotnik's Mean Bean Machine among other titles), Puzzle Kombat (can be found on Ultimate Mortal Kombat on DS), and maybe Pac-Attack.
If you want to solve puzzles in an action/adventure game, Beyond Oasis, Landstalker, System Shock 1/2, the Sam & Max Series, Powerslave, HeXen, Strife, and perhaps Legend of Oasis would be good to start.
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