The circle of fifths is a musical tool showing how all of the 12 keys are related. It is based on a simple principle: in the clockwise direction, each new key is the dominant (V) of the previous key. Therefore, in the other direction, each key is the sub-dominant (IV) of the previous key. The outside track is the circle of fifths for major scales, and the inner track is are the appropriate minor keys for the major keys listed. Here it is:

Okay, I've tried this approximately 10 times now. The result of my experiment in ASCII circle creation technique is that I shall create something entirely new. The rectangle of fifths is what follows:
Bb-----F------C------G------D
| Gm---Dm-----Am-----Em---Bm|
| |                       | |
Eb-Cm                   Gbm A
| |                       | |
| Fm---Bbm----Ebm----Abm-Dbm|
Ab-----Db-----F#-----B------E
The practical application of this is extremely fun. One uses what I call a limiter to get all of the chords in which one can play in a particular key (note that this does not take modulations into account). The limiter is composed of all of the keys adjacent to the original key (plus the original key for the slow ones out there). For example, if we play in C major, we can play F, C, G, Dm, Am, and Em chords and it will still be in key. Note that F is the IV chord of C, G is the V chord; C, G, and F are the primary chords in a C major progression.

For some more fun progressions, take a look at II-V-I progressions. They're wonderful, plus they make you sound more professional.