"You bet! 'The Cage" is the purest expression of Gene's vision--before the evil suits forced him him to dumb Trek down by adding more action and making less cerebral. That Kirk guy isn't the real captain of the Enterprise. And everyone knows Mr. Spock guy is just a rip-off of Number One!" (Wow, that rant practically wrote itself.)
I assume we mean the series and the films only. TOS(And The Cage) Yesteryear TOS Films (I simply handwave The Final Frontier being Kirk's dream) TNG TNG Films DS9 VOY (Minus Threshold) ENT (Trip didn't die, damn it. It was a Section 31 ploy.) First bit of the nu!Star Trek. I know there are some people who insist that anything after Generations is a lie, because Picard's still in The Nexus or something. I also consider Abramsverse an alternate timeline, so I didn't include the Abramsverse bits of Star Trek (2009) in.
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.)
none of it is true trek. fans have argued about it for so long that it has become meaningless. i vote for Seaquest
It's all Star Trek, every bit of it. Some of it interests me a lot more than other parts, but that's a different story.
It's all trek for me. My love for some is more than others. Some I haven't watched in a while, but others I have watched a lot.
Each part of the Trek-verse is meant for different sections of the population. That way there is a little for everyone. Personally, I didn't care for the TOS BUT that may be because I grew up on TNG. The later ones took some time to get into and once I did DS9 then became my favorite overall.