Re: 2 player - well, maybe, except for 3 and 4 player gaming.
Oh. My. God.
Jonah Lomu Rugby by Codemasters, played on a PS (One as it would be now).
What a two-player game. What a game.
For me, it was the fact that you needed a *completely* different approach to 1- vs 2-player modes, as you couldn't just bung it out to the left winger to hand off and score.
Have just looked it up on Wiki, and now remember that we would also try to unlock the special classic matches together, to allow access to ridiculous teams that would make play nothing short of a riot. Brilliant.
That and Sensible Soccer. And my personal favourite was a special version, given away on a cover disc once of Amiga Format (?) that was WW1 Sensible Soccer, playing with a live hand grenade. This would occasionally throb and then explode, taking out and removing any nearby players of both teams, making onward progress rather tricky. Best 2-play I personally ever played. Hilarious.