If it's Summer Olympics, then I haven't much experience having only watched the Women's Gymnastics mostly in 2008 (ehem, Shawn Johnson). I'll get back to you after this year's games.
As for Winter Olympics, I like almost everything. Any form of snowboarding, and a few of the Skiing events are the most fun to watch. Then of course Men's Speed Skating, because Apolo Ohno has been one of my favorite athletes since Salt Lake City.
Curling has always been a favorite sport of mine, and I have no clue why. Maybe because where I am from we don't really have it. I think it is an under-rated sport that involves a lot of skill and strategy.