Some splitscreen multiplayer games I've played and enjoyed:

• It Takes Two - 2 player couch. Amazing game
• Octodad - 4p. Every player controls one or two limbs of an octopus, who needs to pretend to be a normal father
• Nom Nom Galaxy - 2 player couch, 4 player online. Land on an alien planet and build a soup factory. Collect ingredients and fight against another corporation.
• Crawl - 4p. One player is a hero running through a dungeon, the other players control monsters trying to kill them. Whoever kills the hero then becomes the hero. Whoever kills the boss first, wins. Great soundtrack and art.
• Stick Fight - 4p. Competitive yet silly ragdoll combat game
• Magicka 1 and 2 - 4p. Wizard game, create spells by mixing elements and blow up a bunch of goblins.
• Stikbold! - 4p. Dodgeball game, a decent bit of skill involved. Can fight each other or against AI.
• Tooth and Tail - 4p. An RTS game that works well on controllers, you control an army of woodland creatures and have to kill / eat the others. Great soundtrack and art. Can play PvP or against AI.
• Lovers in a Dangerous Spacetime - 4p. Work together to pilot a spaceship and kill monsters and save people.
• Guns, Gore & Cannoli - 4p. Arcadey shoot lots of zombies side scroller.
• Treadnauts - 4p. Fight each other by driving tanks on walls
• Ultimate Chicken Horse - 4p. Design a shared platforming level with traps, so that you're able to get to the end but the other players can't.
• All the Lego games - 2p.
• Stardew Valley - 4p. Grow a farm and befriend villagers
• Speedrunners - 4p. Just run and do parkour faster than the other players
• the Trine games - 3p. Cooperative adventure / puzzle game.
• Wizard of Legend - 2p. Wizard roguelike
• Boomerang Fu - 4p. Fight each other by throwing boomerangs
• Kingdom Two Crowns - 2p. Side scroller town builder, protect your town against the evils outside
• Spelunky - 4p. Roguelike, delve into a cave searching for gold and riches