The great thing about getting into the Paddock area is how close you can get to the equipment. The design and engineering of the cars and equipment make for some pretty cool still life photos. I also group my crew member shots into this catagory.
Most of my speed shots are from during practice and qualifying, I'd rather not get distracted during the race, plus it is hard to take a good shot from the grandstands without annoying your neighbors.
These pictures aren't the greatest from a setting and composition point of view, but I like to get pictures of drivers when they are going about their daily business in the pits. I think its more fun and less intrusive than getting autographs. (but we occasionally do that too)