TNG is my *absolute* favourite. My reasons? Here I go:
1- The space exploring theme is very very appealing to me. In fact, it is maybe my favourite topic when it comes to science-fiction. As an exploration and diplomacy-oriented vessel, USS Enterprise D fits just perfectly for it. Discovering mysterious dyson spheres, dealing with rogue AI issues, navigating deep space areas while avoiding ionizing radiation hazards, dealing with warp engine limitations (they are magic fast but not teleportation), applying safe and non-lethal solutions when stumbled upon foes, looking for our DNA origins in distant worlds... amazing. Just amazing.
2- Captain Picard is just... perfectly well-balanced without falling in the "too perfect hero" cliche. Authoritative but not plain and still accesible and empathizing, wise but willing to make quick choices without enough information if found in dire straits, almost as sharp, clever and insightful at analyzing as Data (who outpowers him when it comes to sheer processing capacity)... and I can go on. While he probably didn't experience much of an evolution throughout the whole series, his character is so dense that you really need several seasons to really get to know him. Plus, Patrick Stewart (Royal Shakespeare Company member) is no joke, he's a really good (and good looking lol) experienced actor.
3- There is enough evolution and good taste in characters (really charismatic). To me, Data is just brilliant. I even had a crush on him lol. His evolution throughout the series is amazing as my namesake @kasspurple pointed out. Plus, holy molly, he's literally a sex-machine

He's one of the more charming approaches to full AI androids I have ever seen. Worf experiences a lot of evolution too. Troi experienced a lot of maturing too. Crusher (oh boy he was so cute... another teen crush lol) and LaForge were rather nice characters although they were not as deep as others.
4- While pointed out as a downside by other posters, I find quite appropiate not focusing too much on relationships between characters when it comes to this kind of science fiction. It's just my opinion, but after all (specially when it comes to humans)... people is people, just placed with better tools (better technology) in more exotic (spacial) scenarios. So for me, the real crux is in novelty and discoveries rather than in (somewhat predictable) squabbles between the guys.
Taking a look at the other series... my thoughts:
-TOS: As another poster said, just way cheesy to me. Also didn't like much Captain Kirk character. Many shallow stories.
-ENT: Same as with TOS but for the cheesy part. I don't like Archer that much. I don't like the pre-federation era (losses a lot of interest).
-VOY: While I love Kate Mulgrow as Red in OITB, I don't like Janeway character. Same for the rest of the crew, I miss so much a charismatic crew... The first season bored me, so I didn't get further.
-DS9: I saw several seasons, but the fact being on a space station instead of a space ship... is a big downside for me (no space exploration). Also, even when introducing many new alien races may sound like a good idea... the vast majority of them were so much anthropomorphic for my taste (in fact this is something I dislike about all the ST series) that it lost the point.
By the way, sorry for the lenghty post