Terminator is a very good case of this. By rights, a sequel likely should have sucked since it's like a horror movie with an iconic villain, rehashing the same premise again. Amazingly enough, there was enough new there that it was a really good movie. What I love is how if you went into the movie knowing nothing, Arnie seems like he's still the Evil Terminator right up to the point where he guns down the T1000 in that service passage in the mall. Yeah, it's hard to not know that going in but imagine the WTF moment if you're watching it clean. If Arnie's the good guy, who the hell is the other guy?! Really well-done. Some purists hated it but I think they're being too picky.
But at this point, after T2, after the damn story has been capped, you really can't do another time travel Terminator. If they were going to tell another story, they had better place it during the machine war. And T3 was pretty much as awful as T2 could have been. Stupid, needless, unwatchable. Not to mention that the whole machine war timeline you're watching is supposed to be undone by the events of the prior two movies so we're in a case of a Seinfeldian movie about nothing.
Salvation at least did what should have been done, covering the machine war. But again it was handled poorly, oh so poorly. And the whole bit with the Sam Worthington character was so pointless and dumb.
The problem with Terminator is that sequels run into prequel problems. Prequels as a rule tend to be awful because you already know how it's going to end because it has to mesh up with the beginning of the prior film(s). But in the case of a time travel story, the future is the beginning of the story and so the whole thing can suffer from that problem, especially as you get closer to the "start" of the story in said future.
All that being said, there's some pretty cool expanded universe stuff for the Terminator series, fan-written. http://www.goingfaster.com/term2029/
Has a lot of trivia directly related to Terminator, the official products, and speculative worldbuilding to determine just what the timeline was leading up to 2029 and the defeat of Skynet. Just what would have happened when Skynet went self-aware? How would it have built armies in the aftermath of the war seeing as it probably wasn't designed and equipped for that precise sort of thing? How could humans have a chance of defeating a superhuman AI?