Unless there's some pressing issue (bathroom, phone call, nuclear winter), I always try to stay to the end of the credits after a movie. Only a small fraction of the reason is to honor those involved in making the film -- I don't recognize more than the tiniest fraction of the names anyway, so it's really just symbolic recognition.
A larger reason is to get the "monk's reward," if any. The monk's reward is what Ebert calls the extra scene they add after the credits, or during the credits -- so-named because of the "monklike devotion" it takes to sit still throughout the credits scroll.
But for me, the primary reason is to use the credits as a psychological cooling-off period, letting my mind wend its way back into reality, and start to process what I've seen. While I'm watching a movie, I rarely analyze what's going on; I just sit back and absorb it, and do the analyzing later. Most of the time, I can't express more than an extremely general opinion of a movie until at least a few hours after I've seen it. The best I can do is "It was good" or "Ehh, I didn't like it so much" or something equivalent.
Sitting through the credits lets me decompress a little bit. Shake off whatever tension I've worked up from watching the (presumably) tense climax. Start working through the movie in my mind, the dramatic implications, remembering scenes I liked or didn't like, beginning to construct an opinion. This isn't a hard-thinking process; it's just sort of the natural coagulation of the experience into something more solid. But I find that sitting through the credits helps me do that; I don't feel like I'm in a rush to get to my car and leave.
It also helps when the theater has plenty of legroom, so that other departing patrons don't disrupt my reverie by kicking me in the shins. Ow.