If it's a private or one-on-one RP, I try to leave it alone, because lurking around those makes me feel dirty. If it's an open RP, I'll sometimes latch on like a soap opera fan until the thread dies, or if it's the sort of thing I can get into I'll start playing in it.

I used to read every dead RP thread on forums too, pages and pages of them, because the more material you encounter and experience, the more experience you'll have to draw from in making up your own stories, plot lines and characters.

That, and some of them are just really fun to read. I've read some awesome stories in old RP threads. I like too how you can see someone's (or even your own) RP skills go from crap to godly over the course of several RPs. It's like watching their inner storyteller grow up and evolve, right in front of you.