The other reason why power chords are used so often in punk, rock, etc., is that they are not really chords, but only a single voice. Explanation:
When standard four-part harmonies were starting to come around, one of the rules invented was that "two perfect consonances of the same type should never follow one after the other" (according to Johannes de Garlandia, c. 1300). This was because the two voices involved were effectively reduced to a single voice, since they each carried the same tune only at different pitches. Doing so is called parallel fifths or octaves and is to be avoided at all costs in four-part harmonization for that reason.
The reason why this only applies to perfect consonances (i.e. perfect fifths and octaves) is adequately explained by e-troom's writeup - the fifth and the octave are harmonics of the root note.
What does this mean? Punk music usually consists of a singer, guitar, bass, and drums. More often than not, the guitar plays power chords, and the bass plays the root note of those chords. This leaves us with a grand total of two voices - the singer and the guitar power chord/bass conglomeration. Wow. This kind of stuff was last seen in the thirteenth century. The songwriter needs only to harmonize two voices instead of the standard four, and the end product is extremely easy to play.
Of course, some more advanced punk bands (such as Green Day) will add background vocals or spice up the bass line a bit, and then you end up with three or four voices. That is actually better than most other forms of modern non-orchestral music, save Jazz and progressive rock.