Chances are you've played at least one game that has been really different than all your other games.
For me I'd say either Katamari Damacy or Psychonauts. Katamari is really one of the weirdest games that there is in existence but there is just something about it that makes it really fun and addictive once you get the hang of it. As for Psychonauts, it was just one of those games that was original and genuinely fun. But it got ignored by a lot of people.
Discuss.
I played Castle Crashers once at a friends house.
It's wierd, yet addicting.
Sentinel Returns for the PS1. Unplayable, but unique.
Earthbound - Most different RPG I've ever played. Sure it's got the basic themes, but everything else is unique.
Boom Blox - Mostly because of new hardware.
Any SMB game - It's a fighting game, but DEFINITLY not in any traditional terms.
Iggy's Recking Balls. One of my favorite N64 racing games.
SSB was unique when it first came out.
WarioWare: Touched! was very unique to me when I first played it.
Cubivore
Stretch Panic and Mr. Mosquito are tied.
Halo.
Oh, wait.
I can not think of any that really sparked my interest or curiosity.
I dunno, maybe Jet Grind Radio.
Glover was quite an odd game...
No More Heroes
I-Fluid.
What do you control? ::)
Smash bros and warioware was really interesting and funny to me when i first played it on the gba.
A tie between Chibi-Robo and We ♥ Katamari. Both were(n't) made on drugs, and both are unique, in different ways.