[Looking for] Shared/split screen games mostly on PC(for gamepads) either PSX/PS2

Distance is a survival racing game (early access) with split screen.

Dirt 3 has local splitscreen racing.
Screencheat is the most unique splitscreen game out there.
Left 4 Dead 2 and Unreal Tournament 3 both have split screen mods that are easy to find.
Awesomenaughts is a 2D platforming MOBA-lite that supports up to 4 way splitscreen.
Portal 2 has a huge amount of content (including Workshop levels) for splitcreen.
Guacamelee!is a 2D platforming brawler that can be played co-op.
Risk of Rain is a rouge-like that supports local co-op play.
Trine and Trine 2 are perhaps some of the best local (or online) co-op games.

Why not try Screencheat

Edit: Forgot to mention that as far as I'm aware its multiplayer only and there are no bots, it recently had a massive discount on humble bundle so there should be lots of people playing online anyway.

awesomenauts, dynasty warriors, broforce, lara croft guardian of light, nba2k, isaac rebirth and fifa.
Those are the games that i liked playing on PC with splitscreen

All fighting games then and racing with coop. King of Fighters XIII, BlazBlue games, Ultra Street Fighter, Skullgirls, Dirt Showdown, Brawlahia, Grid, Grid 2, etc.....

http://www.co-optimus.com/index.php Will let you search by platform and co-op type amongst others but you'll have to go elsewhere for info on controller support

Monaco, Hammerwatch, Contagion, FORCED, Castle Crashers

PS2: Marvel Ultimate Alliance, Star Wars Battlefront 2, Tekken Tag Team Tournament