Performance Based Videos
A Performance based video is a video that features the artist/band/group throughout most or all of the video. This is probably the cheapest 'type' of music video to make, if you can find a suitable location or place to film.
An example of a performance based video is "Best Of You" by the Foo Fighters.
Narrative Based Videos
A Narrative Based Music Video is a video that attempts to tell some sort of story through what is shown on screen. It may or may not fit in with the lyrics, but generally would follow the lyrics in some way. They can often be used if a song features in a film, with clips of the film often appearing in the Music Video as well.
An example of a Narrative Based Video is "Always" by Bon Jovi.
Concept Based Video
Concept based Music Videos are videos that are based around a single 'concept' or idea. They generally take on an unusual form of filming or editing technique that splits the apart from the other types of Music Video. It is rare for there to be a Music Video that is purely conceptual because videos with a performance or narrative base generally get a better reception from the public. An example of a Concept based video is "Monkey Drummer" By Chris Cunningham and Aphex Twin.