Re: C Am F G7
You've found what some people refer to as the "doo wop" chord progression (I-vi-IV-V). It was used in a lot of early rock and roll ballads ("Earth Angel" and "All I Have to do is Dream" come immediately to mind). It's still pretty common.
If you want to practice it in a couple of different keys, do this:
Key of G: G Em C D (or D7)
Key of A: A F#m D E (or E7)
Key of D: D Bm G A (or A7).
"Just because you've always done it that way doesn't mean it's not incredibly stupid." - Despair, Inc.