Whoa, I’d completely forgotten about this old thread. And most of these answers, haha!
I’m positive it’s mostly nostalgia talking, but I’ve always loved the Original Series most of all. It was my first, and it opened my eyes to the possibility that sci-fi could be philosophical, non-war-focused, and optimistic. Everything I’d seen before was either combat-focused (like Star Wars) or kiddy (like Lost in Space), and the original Star Trek was a landmark moment in my personal development. I’ll throw the Animated Series into this slot too, it’s a great series and I highly recommend it to anyone into Star Trek. The writers made great use of the animated medium to create more fantastical aliens and tell stories that would have too expensive in live-action, like underwater exploration and massive pre-Colombian city-planets.
TNG is my next favorite, and it’s probably a better overall show than TOS. The characters are more three-dimensional, the writing was more cerebral, and it had enough seasons to really come into its own. I’ve only seen a bit of Voyager, DS9, and Enterprise, so I probably haven’t given them a fair enough shake, but Voyager was my favorite of the three.
Lastly, I’ve been watching Lower Decks with my free month of CBS All-Access, and I’m pleasantly surprised by how enjoyable it is to watch. The writing is good, the jokes land, and the creators are clearly massive trekkies because they pepper a ton of subtle references into every episode. The characters are all likeable and the plots work both comedically and within the confines of the Trek universe. I didn't go in expeccting much, but now I can't wait for the second season.