This is a sort of counterpart to the Adversarial DM discussion.
What traits would you say define the "Adversarial Player"?
I've seen two flavors of this. Some player seem to play as if they were in competition with the other players, and strive to make the most powerful character. I had a player who wouldn't be satisfied unless his character had an AC at least five points higher than anyone else in the party, and hated the fact that his character could actually fail a Saving Throw.
The other sort is adversarial towards the DM. That is, they seek to "beat" the DM, often through rules-lawyering or flat out cheating. Some go so far as to try and derail the campaign, to prove that they're "better" than the DM on some personal scale.
You, of course, are free to supply definitions and/or examples of your own. That's kind of what this discussion is about, after all.