I'd add this to my list as well, completely spaced it. Resident Evil 5 isn't really that bad (especially Gold Edition). While I preferred 4, 5 wasn't a bad game.
Ironically I was going to buy that one for my Xbox 360, however I waited...glad I did lol. I am highly considering buying that one as well. I definitely look forward to buyign Resident Evil 6 in November =)
Infamous series, God Of War series, Uncharted series, Jak and Daxter series, Ratchet and Clank series... Sly Cooper series, Heavenly Sword, MGS4 + HD Collection, Little Big Planet 1 or 2, Twisted Metal, Resistance series & Killzone series.
I have seen a lot of people say uncharted is great. Will I have to start from the first one to understand and enjoy them all?
I wouldn't say you have to start from the first one, but it's for the best and they're all great games so you'd be doing yourself a disservice to skip any.
I don't know if this is your only console or whether you have a 360/good enough PC so I'll separate into two lists:
God of Wars
Metal Gear Solid 4 (get the HD collection too if you haven't played them)
Assassin's Creed 2 + Brotherhood
Red Dead Redemption
Batman: Arkham Asylum
A Call of Duty or Battlefield 3
GTA 4 (probably better waiting until 5 now though)