Where I'm from, we always sent letters, but I never liked that approach much. It allows the recipient to compose his or her thoughts before replying, but it's also very passive. If you care about somebody, ask them out in person. Might hurt more, but it's a quick cut, and you'll know more quickly than someone who might dither on writing back to you promptly.
I never did much in the way of dances growing up either. Too busy.