I would say that Star Trek: The Wrath of Khan is a follow-on to the original series, with the same cast, and better than any of the original episodes.
Batman (1966) was actually made between the seasons of the TV show, not after it had been taken off the air.
I liked Maverick (1994) but that was a re-boot (with one returning cast member).
The Muppet Movie is a gold-star answer.
Madelyn Rhue (“Lt Marla McGyvers,” or “Mrs Khan”) was not in the movie.
But her off-screen death was one of the big drivers of Khan’s insane lust for revenge, so it still ties in.
Does Wayne’s World count?
The Simpsons movie was pretty good.
Beavis & Butthead, South Park and Borat were pretty good.
Hard to beat Naked Gun, though.
Saw this thread and thought “Well, I know what I’m going to suggest…”
Damn, ninja’d by the very first post.
Next would be the even-numbered Star Trek movies: Khan and The One With The Whales and the Christopher Plummer Quoting Shakespeare one. And you can’t beat a drunk Zephram Cochrane!
Interested in explaining?
I’ve met a few folk who simply said all of Firefly was not their cup of tea, but I can’t recall encountering anyone who felt the movie was significantly lacking compared to the series. Sure, some folk prefer one over the other, but I’m trying to figure out why someone would feel as strongly as you.
Also, G.I. Joe: The Movie (1987).
Cobra-Lalalalala!
Head?
The thread is about GOOD movies! 
While some of the ones mentioned are probably better, I’d put in a vote for the Wild Wild West movies (with Conrad and Ross Martin, not the Will Smith abomination). They kept the feel of the show without being too much overboard.
Pity that Michael Dunn had passed away by the time the first one was filmed. 
I know.
Paul Williams was a fair substitute, times being what they were.
Yes, he built a nuke in the 1880s.
Miguelito could shrink people to small size, create plagues that could kill all life on earth, and live inside paintings. I guess making a nuclear device before the math had even been invented isn’t that unbelievable.
Now, Shields and Yarnell as robots, I got no defense.
I’ll agree with this and add Pee-wee’s Big Adventure to the list.
I’m pretty sure the TV show followed the movie, up to which Pee-Wee was just a cult comedian.
I was going to mention the X Files movies, but the OP asked for “best”.
Hah, you’re right. Mostly. The stage show The Pee-wee Herman Show was first, and HBO taped one of the showings, so it was on TV before the movie. But I’ll admit, that doesn’t really count.
So I’ll replace it with El Camino: A Breaking Bad Movie. It was a nice resolution to Jessie’s story.
Miami Vice.
Count me as another that does not agree.
Yep, back in the days when I couldn’t afford cable and was limited to analog broadcasts. I thought it was a big deal when KTCN and KLXI came on the air and raised the number of channels I got from five to seven. 
The South Park movie came out after the show’s second season. It’s still on the air, in its 25th season.
Not an answer that will mean much to most Americans, but the British TV show The In-Betweeners had two movie sequels, both with the original cast. The second one was good, and actually come to think of it somewhat under-rated, but the first one was a very funny movie that could work without seeing the TV show. It also didn’t feel like three episodes cobbled together, as some movies from TV do.