Bad Mojo - you play as a neurotic greedy skinny guy who turns into a cockroach and has to navigate through a vile apartment only to find out interesting stuff about his life, and get to know that the building is about to blow up. It's... weird but I like it.
Deadly Premonition - no need to introduce, I love this fucker to no end.
Dick Sucks: Terror In Titfield - yes, it exists... A sidescroller where you play as a penis commando avoiding condoms ant pairs of jugs, all disembodied of course. Eeeeeeeeehhhhh...
Yume Nikki - one of my favourites, you explore the dreams of an antisocial girl, and oh God what you find there.
You Have To Cut The Rope - a free title, just go play it and then shake your head in disbelief. It's umm, short alright.
The Binding Of Isaac - oh boy, this one's also very addictive.
Rez - some people call it art and a classic rythm game, but after playing some not-so-classic rythm games like the BIT.TRIP series, I am actually convinced that there exist rythm games that have something to do with rythm. Rez simply doesn't work for me, it's just weird. And the sequel was pffff, let's not even go into that. Oh, and let me remind you of:
The BIT.TRIP series - I actually suffered from optical illusions after playing RUNNER's longest level and trying to get all the gold for like an hour. When I looked away from my screen all the world around me seemed to... warp or something.
YARIS - a free XBLA title, and i still feel ripped off. At one point you are driving a Toyota Yaris with a mechanical arm attached to it that is able to shoot in a tube-like gravity altering racing track, racing against nothing and trying to avoid huge fat guys on a small bike who only wear a barely visible speedo. My. Fucking. God. Oh, and it's pretty much the worst XBLA title, if not the worst of all games in both of the XBOX consoles' lives.
The Legend Of Kage (not sure about the title...) - an NES game where you fly around (because fuck that if that's a jump there) killing the shit out of other flying ninjas, some of which can shoot fire out of their mouths.
Star Wars Chess - there's a nice collection of videos on youtube showcasing every "conflict animation". These include melting some players, beheading them ad other spicy things. You know, everything we loved in Star Wars and all.
Phantasmagoria: A Puzzle Of Flesh - I HEARD THAT CURTIS!