For example, Barbara Bouchet, who went on to play Moneypenny in the 1967 version of Casino Royal (the funny one). And, according to her Internet Movie Database page, she's been busy with work. On Star Trek, she played an evil Andromedian in "By Any Other Name."
And there was Barbara Babcock who was in two episodes: "A Taste of Armageddon" in season one and "Plato's Stepchildren" in season three. She went on to be on Hill Street Blues and Dr. Quinn Medicine Woman. (Technically she was in more than two episodes, often lending her voice to computers, energy beings, and even cats.)
Vic Tayback was in "A Piece of the Action" episode and went on to star in the sitcom Alice.
"Friday's Child" had Julie Newmar. Not sure how famous she was because I think she was already playing Cat Woman on Batman.
Speaking of Batman, Frank Gorshin was in "Let That Be Your Last Battlefield." Again, I think he was already playing the Joker on Batman.
I thought for years that Peter Graves of Mission Impossible played Akuta in "The Apple." But apparently it was Keith Andes (never heard of him). However, in the episode is a young David Soul, who played Hutch in Starsky and Hutch.
And in the penultimate episode (as aired) "All Our Yesterdays," is Mariette Hartley who went on to tout Polaroid cameras in ads with James Garner. The ads were so popular that Hartley did a guest appearance on The Rockford Files.
I could go on; I can think of at least two more. But I won't.
CORRECTION: Frank Gorshin played the Riddler on Batman.