[edit: misread topic, thought it said "favorite 'three' games"]
Star Control 2: The Ur-Quan Masters [http://sc2.sourceforge.net/] - Re-released in a free form, I think this would go on my "favorite games of all time" list, and not just my "favorite free games" one. There may not exist another game with as much epic win to it.
Dwarf Fortress [http://www.bay12games.com/dwarves/] - It's obtuse as hell, and genuinely punishes its players with crashes and unavoidable learning experiences, but it's still one of the deepest and most interesting simulations in existence.
Psychonauts [http://www.gametap.com/play/gameDetails/000475950] - It's been free through GameTap for awhile.
Cave Story [http://www.cavestory.org/] - I'm not drooling over it as much as some players might, but it's nonetheless a little dose of magic that was much appreciated.
Nothing that hasn't already been mentioned, I suppose. I guess if it wasn't really, really good, I wouldn't mention it as my favorite.