Abe's Exoddus (1)
I just revisited the second installment in the Oddworld series of games, and the last I played - the third and fourth, sadly, are only available for the Xbox. If you like platform games at all, this quirky mix of ironic oddness, fascinating story and character design, tough puzzles and fast paced jump and run episodes will entertain your for many, many hours. And even if you don't, you'll have to appreciate some of the lovely, innocative ideas in game design.
Also pretty cool is the list of influences the game designers list on their website.