Now, first we have Stewie Griffin, from the Family Guy cartoon. This cartoon family "lives" in Rhode Island, which is I guess the closest one can get to Massachusetts for a cartoon character; therefore Stewie represents the New England Patriots. Note that William Shatner on Boston Legal has been in a cartoon, but not recent enough for many of the viewers to remember.
The Underdog character has two different aspects of symbolism. He represents the New York Giants, they being the "underdog" in this match. Also Underdog was an anthropomorphic canine version of Superman. People even used a similar catch-phrase: "look up in the sky - it's a bird, it's a plane... it's a frog." Superman lives in the fictional city of Metropolis, which is more or less New York. So we have the underdogs from New York.
Now why Charlie Brown? Obviously the Coca-Cola company cannot have an ad that picks one team over the other. But why Charles, and what's the football connection? As you may remember, Lucy Van Pelt is always pulling the football away from "Chuck" before he can kick it.
Oh, and hey, you've got to hand it to Charles Monroe Schulz, for having Patricia Reichart as the first lesbian cartoon character.