In the Axis of Awesome video, they're playing E (1), B(V), C#M (VI) and A (IV). In other words, they're playing the major chord built around the root note of the key (E Major), then its fifth, minor sixth, and fourth.

There are literally hundreds of songs built around those four chords:
In other keys, it's:
C G Am F
D A Bm G
A E F#M D
F C Dm Bb
G D Em C

Heart of Gold by Neil Young is one (G D Em C)
Let it Be by The Beatles (C G Am F)
Another Girl Another Planet by The Only Ones (E B C#M A)

etc; etc;