Even more than handhelds or video games, when I'm not writing or doing something for classes, I try to find my way onto Kongregate as much as I can. It's changed so much, I remember when I accidentally found it during the pre-Alpha stage before it had the points system and then later they unwisely made rating a game worth 5 points and a glut of high-level users arose. It's still a work-in-progress but I like where it seems to be going :)

For me, what I love about the site is that it has all the flash games I love from across the internet in a single place where (at least with Firefox locked and loaded), there is no weird spyware to clog your system.

Here's a few of my personal picks for most enjoyable games.
Bloons
That goes without saying - I recommend the sequel and the Tower Defense version of the game.
Bowmaster Prelude I wasted sooo much time on this one.
Possibly one of the best zombie games ever made in the flash medium - Boxhead 2Play The More Rooms version is also very good.
The Last Stand - the other really great flash zombie game. A lot easier though.
Swords and Sandals 2 - my most played flash game all-time, it makes my computer sweat. Amazing game but it is a system hog.
Newgrounds Rumble - despite my misgivings about Newgrounds (except their music offerings), this is a great, SSBM-style fighting game.
Ring Pass Not - great game, an inventing and very challenging puzzler, I've never gotten very far with it but I've tried soooo many hours...
Amberial - best the recent games uploaded.