The worst (that is to say, most glaring) example I can think of this is Alien 3. Aliens is the greatest sci-fi actioner ever made. Like all great action movies of the 80's, its greatness lies not only in having incredibly awesome fight scenes (not to mention effects, soundtrack, acting, script), but in having a solid emotional core. This emotional core is the relationship between Ripley and Newt. The reproductive cycle of the Alien is the perversion of motherhood that Ripley has to reclaim for humanity. Alien 3 stomps all over this core by killing Newt. You can't watch Aliens now without knowing that, after all Ripley risks to save her, Newt is killed immediately after the end of the film. This cheapens Ripley's efforts in the one film, even though it was the poorly-made sequel which reduces it.
Likewise another great James Cameron sequel: Terminator 2. Still, ten years on, the most modern looking film put to celluloid. A great actioner with a great core theme: The future isn't set. You can change your destiny. The road for humanity to redeem itself is still open. Along comes the risible, pathetic, budget-looking sequel, and stomps all over this ideal. The future IS set. Your destiny is already written. Humanity can't save itself. In other words: The last movie had it all wrong, even though it stomps all over this one with enormous robo-boots.
Sorry, I'm probably digressing a little bit. This is mainly because I don't have a great deal to say about Ring 2. It's not very good. It looks good (it's well shot), and I suppose there's some initial creepiness, but about halfway through it goes majorly off the rails and turns into A Nightmare on Elm Street Part 2 (the one where Freddy is trying to get into the real world by inhabiting that guy's body? and then he succeeds and like, is incredibly un-scary in the real world? R2 steals this plotline quite unashamedly).
It actually kind of becomes unrelated to the first film (which was about the tape) and just starts making no sense. It borrows all the symbolism of the first film, but whereas that film cleverly combined those symbols into a logical whole which explained everything, this film explains nothing, and is really just a succession of unrelated scenes that are attempting to be scary. But here's the thing: The first Ring was actually, genuinely creepy. One of the only creepy American films to be made in the last decade (the other one that comes immediately to mind being The Sixth Sense). And the reason it was creepy is because it wasn't about cheap shocks, but more about creating a mystery that slowly untangled.
By giving Samara an entirely new, unexplained set of powers and motivations, this is one of those awful sequels that is not only a poor movie in its own right, but actually reduces the impact of the first. If you enjoyed the first Ring, do yourself a favour and keep your good memories intact.
This is a 
I think you mean T3. T2 was still solid.
And lets not forget The Highlander sequals ....
I referred to T2 as a great film.
Ok, got confused about all your referances. You weren't that explicit on what was the good sequal and what was the bad one. Being that you didn't mention the bad one by name.