Along with what others have said:

• Speedrunners
  • Just run and do parkour faster than the other players
• Nom Nom Galaxy
  • Land on an alien planet and build a soup factory. Collect ingredients and fight against another corporation.
• Crawl
  • 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.
• Ultimate Chicken Horse
  • Design a shared platforming level with traps, so that you’re able to get to the end but the other players can’t.
• Magicka 1 and 2
  • Wizard game, create spells by mixing elements and blow up a bunch of goblins.
• Stikbold!
  • Dodgeball game, a decent bit of skill involved. Can fight each other or against AI.
• Tooth and Tail
  • 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 versus or against AI.
• Lovers in a Dangerous Spacetime
  • Work together to pilot a spaceship and kill monsters and save people.
• All the Lego games
• Wizard of Legend
  • Wizard roguelike
• Boomerang Fu
  • Fight each other by throwing boomerangs
• Treadnauts
  • Fight each other by driving tanks on walls
• Unrailed
  • Try to keep a train going by building the tracks as it’s moving.
• the Trine games
  • Cooperative adventure / puzzle game.
• Guns, Gore & Cannoli
  • Arcadey shoot lots of zombies game.
• Kingdom Two Crowns
  • Build a town to protect against the evils outside
• Spelunky
  • Roguelike, delve into a cave searching for gold and riches