We all know the code, but do you include the Select button when you recite it? If so, you might just be a co-op gamer. I return to this bad boy about four or five times a year, because it's easy to excite anybody's nostalgia and get a partner. It doesn't hurt that blazing through the game takes about 30 minutes. Rockin' soundtrack, and gameplay that still holds up, even if half of my friends always forget to duck when the enemy brings a turret along.
Warhammer 40,000: Dawn of War 2
Though I loved the original Dawn of War, the way its sequel shifted to squad-based tactical combat spoke to me a lot more. It didn't hurt that you could bring a friend along for the ride. With two expansions and the glorious Last Stand mode that graced Retribution, this is one of my all time favorites.
The Red Star
This is a good one: based on a relatively unknown comic property, The Red Star is a top-down beat-em-up that also shares DNA with bullet hell SHMUPs. It was originally developed for the Xbox, but was never released (although leaked to the internet). Years later, near the end of the PS2's lifespan, it somehow found a release. It's totally worth playing, and can be found for a pittance.
I can hear Nick's head exploding already. Love them or hate them, the Souls games are unique experiences, and I absolutely love going back and exploring the glorious level design, and screwing around with silly builds to co-op with. When I play these games, I settle into a zone that few others provide. Praise the Sun!