Everyone has to have one (or in my case many) game that they've picked up looked at and put back on the shelf a thousand times. Then on that one day of weakness have bought it, taken it home and been blown away.

Xbox 360:
Call of Juarez. Even though it has a shakey start this game captures the wild west feel better than any other game. It is also pistol centric which is a very good thing in my book (lots of pistols in other words). Lots of really nice touches like distortions on the sniper lens. Loveable characters, a cool postgame & good gunplay. Plus the bible is a weapon. Bonus.

Earth Defense Force 2017: Don't think I need to say anything about this one.

Lost Planet: Pure arcade action. I loved this game to bits though it got a few bad reviews.

Cube:
RE4: Even though everyone praised the hell out of it I was a bit skeptical. I hated the control scheme of the originals. Eventually I gave in and paid a whopping 120 for the special edition alongside Jak 3. I expected to go home and play Jak 3 all night, instead it was a few weeks before I even got to Jak.

Tales of Symphonia: I was quite sick for a while, like coma sick. When I eventually came out of it my girlfriend took me to get a game and against my better judgement I picked up Tales of Symphonia (which had just come out). Three playthroughs later I'm glad I did.

PS2:
Pro Evo Soccer 4: Ever since my parents forced me to play when I was a kid I've hated soccer. I can't imagine what made me pick this up in the first place. I'm glad I did though.

God Hand: Hmmm... review says that most people won't like it... I did like Clovers other games though. I guess I'll give it a try. Now it's my third favourite game ever.

There are heaps more, I'd have to have a good look at my collection though.