Upon rewatching the three Back to the Future movies, I am pleased to report that I still like them. Although the first movie is clearly better.
It helps that I'm a sucker for time travel stories. I really enjoy the twisted logic involved with multiple timestreams and going back to see a previous scene from a different angle. I approve of a movie that gets out of hand to the point where one of the characters needs to break out a blackboard to explain the plot to everyone. Say, have you seen Primer? Man, that's a complicated movie. Good times.
The way I see it, there are three basic ways time travel gets used in stories. And conveniently enough, the three Back to the Future movies cover the spectrum.
The most basic kind is where you only have time travel at the beginning and the end of the story and the story isn't really about the time travel. Like in A Connecticut Yankee in King Arthur's Court, where the protagonist travels to another time, does some stuff, and (usually) comes back. This is the kind of story you get in Back to the Future 3, which I think is the weakest movie. I mean, I like all that train-robbery stuff, but since they've already resolves Mad Dog Tannen's thread to Doc Brown's life, they could have taken their time a little more. On the other hand, I do approve of the steam-powered time-traveling flying locomotive at the end. So that's pretty cool.
Then you get the most common kind of time travel story, where "History has gone wrong" and the goal is to fix it. That's your basic Time Tunnel or Voyagers or Quantum Leap story, and it's what happens in the first movie. Marty has to make sure his parents end up together and maybe get back home to 1985. Incidentally, one of the reasons this movie holds up is that they do a good job of establishing 1985 accurately; it's got all the goofy hair, fashion, and music that you'd use if you were setting a movie in 1985 now.
Finally, there's the full-on Time Travel Phantasmagoria, where there are multiple time loops and half the scenes end up getting overwritten by the end of the movie. There aren't a lot of movies like that (except for Primer, which more people should see, if only so I have people to talk to about what I think happens in it), but there are some science fiction stories along these lines, like Heinlein's "By His Bootstraps" and "All You Zombies—". This is the second Back to the Future movie, where the plot happens in three different eras (and you get to see the same buildings and people at different times, which is always good fun). These stories are usually pretty complicated; look at this diagram for "All You Zombies—", which is actually harder to follow than just reading the story in the first place.
By the way, the reason I decided to rewatch these movies is that I greatly enjoyed this video, which tries to put the "Enchantment Under the Sea Dance" scenes from the first two movies in context with each other. I heartily endorse this product or service.