My fondest gaming experiences have been two+ player:
Worms (makes good friends curse each other: a good thing!)
I don't do PES or FIFA, though I know folk who play little else
Mario Stadium Soccer (bonkers)
The Chaos Engine
GoldenEye 64, and later, Halo Combat Evolved (most FPS games wanted a LAN or null-modem cable for multiplayer. Split-screen gaming is fun and easy)
Special nod to Portal 2, a set of puzzles that require two players to solve.
Hmm, most of these can be divided into Racing, Fighting, Ball Sports or Shooting.
I haven't actually plugged in my console for over a year. I've had a few sessions of Worms with friends, and a lost weekend when I discovered an Android port of Dune 2 (finally, a use for my Galaxy Tab 10.1!), but that's about it!