Making captchas less annoying
I personally find captchas annoying. And most of them are completely inaccessible to people with visual problems. But if you find that you must implement a captcha, you can at least try and make it as painless as possible for the user to use.
First off, let's review what the purpose of a captcha is. A captcha aims to differentiate human beings from bots. As such, there is nothing more annoying than proving to a captcha that you are a human being by replying correctly to it only to be asked again and again when form validation fails for some other field.
So here's a pattern for captchas that should improve the usability of systems that employ them:
If the captcha is valid but form validation fails for some other reason, store the fact that the user is a human being as a cookie or on the server and don't present the captcha to the same user next time the same form is submitted. You can even go so far as to not present that user (based on IP/cookie/session) with captchas for other forms. If you're worried about spammers getting through, you can limit this to a specific period of time (ten minutes, an hour, a day, etc.)
Update: I just saw that Google's Blogger implements a similar pattern to what I describe here in their commenting system and doesn't keep presenting you with the captcha once it's reasonably sure that you're human. Good one, Google! :)