Jazz guitar players tend to play "closed" chords -- chords that have no open strings. For them, a capo is unnecessary, and they sometimes take a disparaging view of people who use them. In any other style, open strings are an integral part of the sound of the guitar. So non-jazz guitar music tends to sound different in different "frames" -- which are different keys when played without a capo. the capo makes it possible to match one frame with a different key, so it's an important tool. Same goes for open tunings -- you can get the particular sonority of a DADGAD tuning in a number of different keys by using a capo.Also, as Willie-O mentioned, using a capo can impact the sound even if you aren't particular about what key you're playing in. A capo affects the tonality of the instrument, and the altered tonality can be just what you're looking for sometimes. Flamenco guitarists always used them (they call it a "cejilla") to match the key the singer was in, but through this they discovered the way it affects the tonality, so that now you'll even see solo flamenco guitarists using them. [Willie-O is also right about string bending; capos severaly limit your ability to do this and remain in tune.]
My capo of choice is the Shubb, because you can adjust the pressure (back off on the adjustment screw as you go up the neck). On instruments with a flatter-than-Martin fingerboard (my Lowden and my Larrivee both share this attribute), it helps if you "customize" it by either straightening the metal bar somewhat, or shaving down the ends of the rubber sleeve that goes over it.