All Trek before Abrams reboot mostly feels like Star Trek to me. Some of it is great, some of it is bad, but I cannot say that any of the series as a whole* or any of the movies were not Star Trek.
But the Abramsverse just doesn't feel
like Star Trek to me. It is like some completely different movie with Trek names and elements pasted on. It is hard to fully explain.
(* Enterprise however really went to directions I didn't like, and the blatant disrecard of the continuity didn't help.)