One problem I've been noticing more and more as of late is that certain archived posts on blogs tend to become magnets for comment spam.
One way to deal with this is to automatically close comments on posts after a set amount of time. That's not a bad thing, but I think there can be a lot of value in comments on seemingly old posts so I prefer to keep them open when possible.
What I tend to see is a lot of spam on a limited number of posts. Most often, this seems to be related to the topic of the post where topics known for being more attractive to spammers draw more spam comments.
If you find that you have some problematic, spam attracting posts, consider disabling comments on just that one post.
Here are two examples of how this can be done.
In Movable Type, find the problematic post in the admin side of your site and uncheck the feedback checkboxes:
And the same thing works for Wordpress: