BuddyPress.org

I had a similar issue weeks ago and nearly gave up on BuddyPress because of it. Today I tried a fresh [1] install of BuddyPress 1.5.2 with WordPress 3.2.1. I did have to wait about five minutes, but the email did come through.

Are you getting any error messages?
Try to log in with the new username and see if you get the error “you need to activate your account” (not verbatim) (Update: The error reads, “Your account has not been activated. Check your email for the activation link” in WordPress, I’m sure the BuddyPress error message is very close)

[1] I didn’t change any settings from their default expect (“Anyone can register”). The only other plugins that are activated are AutoChimp and JetPack, which shouldn’t have anything to do with this issue.

Hang in there! BuddyPress is a young project. If you persist, I’m sure you’ll figure it out.
James