I discovered this really cool site, Chess Personality, that tells you. You take a 20-question quiz and based on your answers, it tells you what style you possess, the characterastics of that style and what openings best suit your style.
How accurate is it? My results look to be about right. According to my answers I'm a technician like Kramnik. Technicians are the quietest and calmest chess players. Strategists who rarely attack directly and prefer to quietly exploit positional advantages, Technicians utilize their exceptional intuition to guide their positional play. Rarely losing control, the Technician exploits almost invisible positional weaknesses to win in the endgame. Technicians do not like to take many risks, and therefore rarely lose - but also win less than more aggressive players. Recommended Openings - White: English Opening and Black: Sicilian Defense; Semi-Slav; Petrov Defense.