Understanding The ii-V7-I Progression

Someone recently asked me to explain the ii-V7-I progression.  Why should I study it?  How and why does it work so well?  When you are done reading this, you will want to practice ii-V7-I's all day long!

The ii-V7-I works so well due, in large part, to a concept called "voice leading".  The idea stems from singers and the notes they sing.  If you have done any singing (and I try not to!), you will notice that it is much easier to sing half-steps and whole-steps than larger intervals such as thirds, fourths, and fifths.  Not only this, but the human ear is more satisfied with melodies constructed with smaller intervals (the reason why some would say that Jazz is an acquired taste).  Voice leading comes into play when observing the movement of certain notes when transitioning through the ii-V7-I progression.

The notes I am referring to are the 3rds and 7ths of each chord.  The importance of these notes is that, aside from the root, they dictate the most fundamental tonalities of the chord (i.e. - what the chord sounds like, as in minor or major).  Take for example, the ii-V7-I progression in the key of C Major:

                   Dm7:  D F A C

                      G7: G B D F

                  CM7:  C E G B

Dm7 -> G7
        The 3rd of the Dm7 becomes the 7th of the G7 with absolutely no movement.  Something I forgot to mention is that the voice, most of all, would rather just be lazy and not move at all!
        The 7th of the Dm7 resolves down a half-step to the 3rd of the G7.  Just a half-step!

G7 -> CM7
        The 3rd of the G7 becomes the 7th of the CM7.  There's that lazy voice again!
        The 7th of the G7 resolves down a half-step to the 3rd of the CM7.  Just another half-step.

Wow!  The ii-V7-I progression is one cool cat!  Time to practice...