If you consider TOS separately from the TOS movies, the only real "regular cast" members were Shatner, Nimoy and Kelley, and by all accounts, they got along with each other just fine. There does seem to have been some professional rivalry between Shatner and Nimoy (publicly acknowledged by both of them) but it doesn't seem to have ever gotten out of hand. And, indeed, the two went on to become lifelong best friends.