I do. My chat clients are set to automatically log, so that when I talk to someone a week later, I can look at the history. More importantly, a lot of questions get asked and answered over IM, so I can check it for answers to "why is X broken" or "How do I Y, again?", or "what was your mailing address?" without having to actually _ask_ the person again.
I've never looked back at archived IMs from years past, though, but they are still squirreled away on the removed hard drives from past machines.
