I think that what I'd do would depend very much on who it was and why I didn't want to exchange numbers.
If it was somebody I liked but just didn't want to chat with on the phone (I am *not* a phone person, I barely call my mom), I'd give my email or I'd suggest that we look each other up on Facebook.
If it was somebody I didn't really like, I'd probably say, "You know, I'm not really a phone person. Seriously, I barely call my mom!" But it was nice to catch up. Bye!"
If it was somebody that I liked but didn't really care to have an ongoing relationship with, I'd probably do the first (email or FB) but mention that I had a lot on my plate and didn't have much time for chatting, so they didn't expect much.