1. I've mentioned Jigsawdoku before. It's sudoku as a jigsaw puzzle. Each puzzle piece is a square tile with a number on it. I like it better than other online options (such as Websudoku, Samurai Sudoku) because it's colorful and has sound effects.
2. Bloxorz will brutally exercise your ability to visualize things in 3D. Many people seem to get stuck on Level 7 - my hint: you need to land on that useless-looking bridge in just the right position in order to line yourself up right for the hairpin turn.
As puzzle games go, this one has an unfinished feel to me. There is no real ending to it; after the 35th level it just stops. Also, because each puzzle has only one solution, it feels limited. You also can't tell whether a soft button is helpful or "you've just lost, throw yourself off the edge" until you try it - and because the game records how many times you try the level, that seems unfair. Overall though, this game has potential to develop into something more interesting than it is at present.
3. Bloons is where you're a dart-throwing monkey who wants to pop balloons. If neither of the above games halts all other activities, this one will. :)
4. Then there's Bloons Tower Defense, which I personally like better because it's more relaxed. You set up your towers and then sit back and watch balloons pop, which is hypnotic and oddly musical, especially on the higher levels. I hope the fine folks at Ninja Kiwi will make more maps (and tower types, and maybe even mobile troop types) for this in the future, or even let players make some the way they can with Bloons.
Also, if defense games are up your alley in general, there is also Defender. It's rather more complex than the Bloons version and has a dark medieval feel to it. It doesn't work on all browsers/platforms, however.
5. And finally, my current obsession is Collapse. This is a frenetic-paced version of the game, where you have to eliminate colored blocks before it hits the top. As levels go up, so does the game speed... It has some similarities to Tetris, but the game it most resembles is Playstation II's Super Puzzle Fighter 2 Turbo.
6. Future obsession? A friend has passed me a link to ClickDragType. I think he's trying to find revenge for all the bloons.