The other day, I looked up the chord sequence for a song I like. It turns out it goes like this:
G, F, C, D, Em, Am, D, G
Looking at the rest of the chords in the song, this is clearly and unambiguously in the key of G major. And, really, the chords aren't anything unusual or surprising.
But look again at the chords I listed. What is that F major chord doing there? In the key of G major, that is an illegal chord. So why is it here? More to the point, why doesn't it sound wrong? Until I looked this up, I had no idea anything unusual was going on. I certainly didn't hear the song and think "oh man, that second chord sounds weird!" What arcane musical theory did they use to achieve this?
(Incidentally, the verse is the only place where this F major chord shows up. Every single other chord in the song is in the key of G major and follows the typical sorts of patterns you'd expect for that key.)