I think only the Mac version of AIM (called IChat) does that.
With the Windows version of AIM, you have to save them manually.
iChat isn't the Mac version of AIM. It's an AIM client that Apple makes. AOL also has an official client for the Mac, but it's showing it's age.
If you want to have similar functionality, you can get DeadAIM, GAIM or Trillian. I, myself, use Adium for Mac. It logs everything for me.