Personally, I don't really care much for baseball caps, although I'll allow as how they have their place (chiefly, as part of a baseball uniform). I have nothing against wearing something on my head, to protect my scalp from the sun's rays during the summer, though - particularly as my hair thins with the passing of the years. Last summer, I got pretty good wear out of a Havana-style Cuenca hat (from http://www.panamahatsdirect.com).
Not trying to convince you to adopt similar headgear, mind you. Although I hope that if you stick with a ball cap, you'll at least avoid those horrible one-size-fits-all versions, with the plastic adjustment tab in back. And that you won't wear your cap backwards, which is a practice just too asinine for words.