"The two-fisted coward" - player with an optimised list that likes to style himself as the biggest fish in his pond. Likes to play against obviously inferior players/lists repeatedly, just to win, but doesn't want to play someone good and will often decry a powerful list as "cheese". Frequents the game stores but not so much tournaments (might face someone better there...).
"The serious tournament gamer" - plays with a max optimised list, practices the crap out of it and plays to win, but plays to beat the best. Travels to tournaments to play the best in the hope of being the best. Doesn't have a lot of interest in playing new players or suboptimal lists, no interest in crushing newbies but wants to find the best opponent he can. Any newly-discovered "cheese" is a challenge to be fought repeatedly until beaten.
"The WAACer" - literally, doing anything they can to win. Often likes tournaments but rarely scores well for sportsmanship. Typically will bend the rules, harangue their opponent or outright cheat. Yuck. Fortunately relatively rare.
"The underdog" - competitive, but insists on taking a suboptimal army/list. Accustomed to losing and often a great sport, but he'll play his hardest so don't underestimate him because he knows what he's doing. A win with a cheesy list isn't much of a win for the underdog, but a win with a bottom-dwelling army is all that much more sweet. The underdog often has a themed army.
"The artist" - he's at competitive tournaments but he's aiming for that best painted prize. He may be competitive or not about the game, often fairly happy to just chill and play (just don't knock his models!), but the paint scoring will have him on tenterhooks.
"The nice guy" - he's there for a good time. Typically great to play against (as long as he doesn't get too distracted telling funny stories to finish the game!). Why does he go to tournaments? Just to have a bunch of good games, meet up at the bar afterwards, etc.