A randomly detemined day in which everything you say means the opposite. For example, if you denied that you were madly in love with Alex, who smelt of poo, your friend could then laugh and say "Haha, it's actually opposite day, so you just said you love Alex!" and then run off to tell the whole playground.
The problem with this was that by saying "It's opposite day" on opposite day, you were actually saying that it WASN'T opposite day. This, however, was entirely beyond our 9-year-old minds, who really just wanted an excuse to tell the entire school that you loved Alex.

A variant on Opposite Day was the Opposite Game. The initiator of the game would ask, ofr example, 'Do you shag your dog? By the way, we're playing the opposite game.'
Answer No : means you shag your dog, because we're playing the Opposites Game, so no means yes.
Answer Yes : means you shag you dog, because we're playing the opposites game, which means that to say "we're playing the opposites game" means "we are no longer playing the opposites game". In which case yes means yes. So you do shag your dog. And you don't even have the decency to try and hide it.

Our school refined the concept of Opposite Day brilliantly. The plan is simple; go up to someone and ask them if they're gay. When they say no, inform them it's opposite day and that they are therefore very, very gay indeed. Coax them into saying "Yes I AM GAY", and then proceed to beat them mercilessly. For being gay.
I still use the basic technique today with my girlfriend when I can't be arsed making a cup of tea. True genius never ages.