mtcp122 said:
You need Super Smash Bros Melee. And perhaps Mario Kart Double Dash.
Call of Duty is actually pretty good for splitscreen giggles, slap it on, 4 player splitscreen and fill it up with bots to avoid the pissants online and have a laugh.
Sonic & All Stars Racing Transformed on the 360/PS3/PC/Wii U is actually a bloody fantastic racer with tonnes of modes and stuff and generally proves to be a hit with most who play it splitscreen, it's easy as hell to just pick up and play it and it lacks any of the obnoxious bullshit from mario kart.
Since you have a PS2 I'll go ahead and recommend that you pick up a copy of SSX On Tour, it only supports 2 players but there's cheats to unlock all the stuff to play with, and the mountain freeride basically lets you dick about, or race down from various points on one huge open mountain and make your own rules and such. Easily one of my favourite PS2 titles for splitscreen.
Resident Evil5 and 6, as maligned as they are, are very fun 2-player co-op shooters. Lost Planet 2 is pretty maligned too but can be a lot of fun in co-op. Once again it's mostly the dicking about factor and taking the piss. A friend and I spent a good half hour questioning why the last boss of Resi 6 is basically a bioorganic terminator, a chimera, godzilla, and mothra all in one....
Oha nd Resistance 3 on PS3 is great co-op and online supports slitscreen too, good survival mode though thats DLC.
My PC recommendation is Civilization 5. Get a few friends in a room for a small lan party, team up with each other and let the chaos ensue.