Mine would have to be Voyager, solely for the premise of being stranded all the way across the galaxy. The ship becoming some sort of self-sufficient mobile town (it even had farms in the form of an airponics bay), trying to get home but also being scientists and diplomats on occasion.
Of course, I've had quite a few "oh COME ON how does a Starfleet captain/officer do/say THAT?" moments. Like when Tom Paris first tried his transwarp drive and started to supposedly "evolve", that's NOT how evolution works THIS AIN'T POKEMON.
But I'm sure that happens to anyone who's watched enough Star Trek, right?
Also the finale was sort of an ex-machina; even though I can get that Admiral Janeway came from another timeline and that her trip into the past just created the one we decided to follow.
Actually, at least one conflict wasn't resolved until some time later, the issue with Maquis members not fitting in with the rest of the crew. I know it wasn't really put in the foreground aside from a few moments, but that doesn't mean it was gone.
Not to mention the new problems; there was the other Caretaker they wanted to find, they had just acquired a new enemy race on their first day in the quadrant... I don't recall all of them off the top of my head.