I'm surprised Cave Story hasn't been mentioned yet. Anyway, Cave Story is my pick because it's pretty much the best freeware game I've played.

Cave Story (aka Doukutsu Monogatari)
Adventure/Shooter

This is an 8-bit game that plays a lot like the old Metroid games. In fact, it pretty much steals the little tune that plays whenever you pick up a new life container to extend your healthbar except for one note. Still, it's a lot of fun, the music's pretty good, and there's a goofy story with a cast that consists of a robot who gives you her panties, talking dogs, and what everyone else who's played the game seems to think is a living toaster that says "HUZZAH!" a lot.

http://en.wikipedia.org/wiki/Cave_Story

There's a link with more info and links to downloading the game and the English translation patch.