Gaming has changed a lot in a short period of time, and it seems like another era when split screen multiplayer was automatically included with any given game. Sadly the practice is now fading as online multiplayer replaces it in the hearts of a younger generation.
Goldeneye is of course the title that will always be instantly associated with split screen, although it also showed the mechanic's limitations: being able to see what your opponent is currently doing. This very issue was actually made into the basis of Screencheat, a game where everyone is invisible so you have to look at other player's screens to have any idea where to shoot.
While a dying option in newer games, there are still titles worth pulling out to play split screen with your friends, from the Left 4 Dead series (which is overdue for a sequel itself) to Far Cry 3.
Thankfully, split screen isn't entirely dead and just returned with the newly released Gears Of War 4 (which is absurdly awesome by the way). As far as I'm concerned, split screen co-oping with my friends while getting drunk is an integral part of the gaming experience. You lose something when your bud is talking over a microphone across town and not sitting on the couch next to you.