A CAPTCHA is an image that is (ideally) impossible for a computer to read but easy for a human. It's used to verify that a user is not a bot, rendering brute-force attacks unfeasible. However, even if it is easy for a human, it's also very annoying. For that reason, you need to use them with moderation.
The biggest technical threat is brute-force attacks on account logins. If someone gets the password of the admin account... well, I don't have to tell you the kind of hurt that can result. Combating this can be as simple as implementing brief (15-minute) bans after a certain number of failed login attempts. I don't think it's feasible to use CAPTCHA in this case because it's something that everyone will be presented with, especially if they don't have their browsers set to keep them logged in. I dislike entering more than a couple of them a day, and any unnecessary ones annoy me. However, if you implement temporary IP bans and change your password regularly, it should afford you a reasonable amount of protection. Other options here may be to require CAPTCHA on all attempts after the first one (decided by IP, not cookie), or to create an account that is used only for administration and give lower permissions to your regular account.
You can use CAPTCHA on registration, but I don't like to spend too long filling out registration forms, either. Besides, a human can register, then let a bot loose on the site. It's still not a great solution, although if you have fairly generic registration forms (or use an unmodified script), that may be a concern.
Instead, I suggest requiring CAPTCHA on a user's first few posts/comments/messages. After the first few, no more annoyances. One idea I just came up with and have yet to implement is simply to require CAPTCHA for all users with a 0/0 ratio. If you're using your account, you're likely not a bot.
No matter how careful you are, some will inevitably slip through. As I've mentioned before, proactively promoting moderators means that what does get through can be dealt with reasonably quickly. This is especially nice in the case of porn spam with images attached, which is never nice to be presented with unexpectedly.
If you have any other suggestions, I'd love to hear them.