This game involves two players the way I learned it, but there's really no reason not to have more. See below.

Player 1 says a word. Any word. It doesn't matter whether it's a noun or verb or adjective or proper noun or whatever.
Player 2 responds with a word that is entirely unrelated to that word.
Player 1 responds with a word that is entirely unrelated to both previous words.
(repeat as necessary)

On each turn, the player says a word which has no apparent connection to anything said recently. A player loses when e says a word which is connected to a previous word - it might be because it rhymes or comes from a similar context, or both describe the same general idea (such as two animals). Additionally, "he who hesitates has lost" - it should be apparent if the frenetic pace of the game is broken by one player.

As you can tell, this game is entirely subjective. You have to be willing to admit you've lost.

I knew someone who was spontaneous enough to always win at this. You really have to let your right brain take over.

It turns out that this game generalizes to any number of people, and is played on the BBC radio show I'm Sorry I Haven't A Clue as "Word Disassociation".