An extension of the side conversation from the Michael Jackson tribute thread. Circle of Fifths is the first question. What is it? Why do I need to know it?
It doesn't look like anyone mentioned this so...
Most musicians memorize the circle of fifths because it helps them remember closely related keys (the keys which are most often moved to and from in a song when the song changes key). Composers move to closely related keys because it creates variation in a piece of music by moving the tonal center, while being the least jarring to the listener. For example, if you write a piece in C Major you can move to G Major fairly easily because their scales are only separated by one sharp key (F# rather than F).
The next question then has to be "why a fifth?" or "what is the significance of the fifth interval?" It is significant because it is the first natural non-octave overtone above the fundamental note. It is the interval that is most harmonious with the original note other than the octave (and the octave isn't very interesting because it doesn't get us anywhere - it's pretty much the same note). If you are interested it might be worth your time to read about Pythagoras and his ancient study of harmonics. It's pretty neat.
This is where I think music theory becomes interesting. The equal tempered "Western Chromatic Scale" (what you and I are familiar with c, c#, d, d#...) was created around the 17th Century to suit keyboard instruments where musicians couldn't alter the pitch of individual notes (because keyboards are essentially a row of switches unlike stringed and wind instruments).
So the octave was divided into fifths C to G to D to A to E... until it we arrive back at C (well almost, they are all slightly flat because the octave doesn't perfectly divide naturally into these 12 segments - but it's close). Essentially these become the 12 notes within an octave on a keyboard instrument.