I don't think I have(or at least can't recall) playing any games that were too weird; as in an really abstract, surreal-ish games. But, I do remember playing a game for the N64(and I don't think it's too uncommon around here, so you might have played it) called Mischief Makers. You basically play as an android-ish green haired girl named Marina(most of the game). In the beginning, your creator and master, Professor Theo, is kidnapped by an empire and you embarq on a lovely little quest to save him. The game takes place on the planet Clancer(sounds an awfully lot like Cancer, lol), where pretty much everything has the same weird face, living or otherwise inanimate. The game spans a multitude of environments, each with their own interesting atmosphere, with a myriad of varying scenarios along the way. It's not really the type of game that's easy for me explain, so hopefully you'll play it if you haven't already, and enjoy it. It's personally one of my favorite platform games of all time.