SNES: Gooftroop [https://en.wikipedia.org/wiki/Goof_Troop_(video_game)], Contra III [https://en.wikipedia.org/wiki/Contra_III:_The_Alien_Wars], The Lost Vikings [https://en.wikipedia.org/wiki/The_Lost_Vikings], Wild Guns [https://en.wikipedia.org/wiki/Wild_Guns], Pocky & Rocky [https://en.wikipedia.org/wiki/Pocky_%26_Rocky] and it's sequel [https://en.wikipedia.org/wiki/Pocky_%26_Rocky_2] would be the ones I'd recommend.
N64: Hexen [https://en.wikipedia.org/wiki/Hexen:_Beyond_Heretic], Perfect Dark [https://en.wikipedia.org/wiki/Perfect_Dark] and Rampage World Tour [https://en.wikipedia.org/wiki/Rampage_World_Tour] maybe? There aren't many options in this platform at least not many I've played.
GC/PS2 multi: Alien Hominid [https://en.wikipedia.org/wiki/Alien_Hominid][footnote]Specially the PDA games, alternatively just get Battleblock Theatre but AH is a good Metal Slug style game.[/footnote]...
I swear I know way more and I can tell them to you later but mid-way through that post I got really sleepy and I think I can go to sleep, I encourage you to ask me again so I remember, I know for PS3, XBOX 360, Genesis, NES and PS2 too, even some Dreamcast and stuff, I had 2 brothers that also really liked games so I know a lot about co-op games, I'm just really tired right now, but I'll Throw in the TimeSplitters trilogy for good measure, think Perfect Dark Co-op but way better, the first one can be a little bit lacklustre but some of the level design is downright masterful like the Japanese house, in some levels even the objectives are slightly tweaked for co-op like the Western in TS2, anyway that's my TOP pick for shooter but I can't in good conscience not mention Trine 1 & 2, 3-player co-op in which each player gets a completely different character, while Single player is cool the game gains a lot more depth in co-op because you have to find a way to get all 3 characters through the map which brings out true co-operative gameplay, seriously solid games and some of the best co-op around, it's solid as a single player, great in 2 player mode and fantastic as a 3 player game.
[sup][sup]If you do ask me I might not reply until Sunday have work and D&D tomorrow and Saturday, though that's another fantastic choice, try a tabletop RPG, best co-op ever.[/sup][/sup]