I thought it would be interesting to ask this question as we speculate on who will come in as an OC. I found the following information on what are considered the 6 offensive systems being used in the NFL today on wikipedia. While this may not be the autoritative source of NFL systems it is still very interesting. Especially for those of us who aren't offensive guru's.
Specific offensive strategies
Using a combination of passing plays and running plays, the offense tries to gain the yards needed for a first down, touchdown, or field goal. Over the years several football coaches and offensive coordinators have developed some well-known and widely-used offensive strategies:
Option offense
Streak and Read Principle Offense (Patriots, Giants, Broncos)
Smashmouth offense
Air Coryell offense
Spread offense
West Coast offense (Green Bay, San Fran, Washington, Philly, etc)
Pistol offense (used by West Coast teams)