According to Peter David's New Frontier
novels, both Kirk and Spock puplished their memoirs after leaving Starfleet. I'd love to read those! (hint, hint, Pocket Books)
The Enterprise-B's Captain Harriman read about Kirk's missions in grade school. And the NX-01 Enterprise crew were doing lots of silly PR work in early episodes (photos of Archer in the captain's chair, making recordings for school kids, Archer writing a foreward for someone's book etc), so these people are somewhat in the public eye.