Are there ways except CAPTCHAs for web apps like pastie.org or p.ramaze.net? CAPTCHAs take too long for a small paste for my taste.
You could try Honeypot CAPTCHAs. Essentially, you hide some form fields using CSS. Your users will never fill out the fields because they won't see them, but spam bots who don't support CSS will fill them out. On the server side you just ignore comments/pastes/etc. that have that field filled out.
In addition to honeypots, you can use timestamps and one-time-tokens to stop replay attacks. Here's a discussion of combining the two techniques.