I play with both hands. I'm mostly righthanded, and that's how I started, but when I got my classical guitar, it was too deep for me to fret it, so I said, well, shit, I guess I'll have to turn it over and learn to play lefthanded. Which I did, and now it's so funny because I have 2 totally different styles.
Also, Hendrix was mostly righthanded (writing, eating, and stuff) but preferred playing lefthanded.