I'd consider Lord of the Rings an exception though since all movies were made at the same time, so it's really just one LOOOONG movie as opposed to a true sequel. Other bad sequels are the original Batman movies. First two were awesome, third = garbage. Stupid Schumacher. I mean nipples on the bat suit? Come on!
I'm still trying to think of good third movies. I think Star Trek 3 is a good candidate. I'd have to say that Scream 3 was quite good as well, relatively speaking.
If I were to guess at a reason for this it would be due to economics of it all. Movie 1 = labor of love. Movie 2 = labor of love + cash-in. Movie 3 = PURE cash-in + labor of hate.
Oh, actually I thought of one. Army of Darkness in the Evil Dead series! That movie is great.