We'll begin with an easy and very popular tune, Van Morrision's "Brown Eyed Girl" (get tab from Musicnotes.com). Here are the chords for the intro and first part of the verse, which comprises a large part of the song:
Gmaj - Cmaj - Gmaj - Dmaj
By studying the above progression, we'll can surmise that the song is in the key of G major, and that the progression is I - IV - I - V in that key. These three chords, the I, IV, and V chords (all of which are major), are by far the most widely used of all chords in pop, blues, rock, and country music. Songs like "Twist and Shout", "La Bamba", "Wild Thing", and many others use these three chords almost exclusively. With this in mind, we can conclude that it is not the chord progression that makes "Brown Eyed Girl" so special, as these chords are used constantly in pop music. Rather, it is the melody, the lyrics, and the arrangement (which includes the song's very famous guitar riff) which make the tune so distinct.