In case you haven't realized by now, i'm a big Minnesota homer, so here I go!
Minnesota vs. Wisconsin for Paul Bunyan's Axe:
The is the longest and most played rivalry in Divison 1A football, dating back to 1890. The Axe didn't come into play until 1948. Unfortunately, those damn Badgers have won the last 4 contests and I can't see the Gophers getting it back untill 2009 at the earliest.
Minnesota vs. Iowa for Floyd of Rosedale:
This one goes back to 1935 and is always heated. Somehow Hawkeye fans manage to drive their tractors up I-35 to the big city of Minneapolis whenever the game is played there.
Vikings vs. Packers:
Cheeseheads are bad. Green Bay fans are fat. Brett favre is a crybaby boozehound pill popper. Skol Vikings!
Minnesota vs. Michigan in the Battle for the Little Brown Jug:
The Battle for the Little Brown Jug dates back to 1903. Michigan fans don't concern themselves with this game too much as they have a wide lead in overall wins, but this game is always big for Minnesotans.
I'm also quite fond of Twins vs. White Sox, Michigan vs. Ohio State, Minnesota vs. U of North Dakota (hockey), and Minnesota vs. Minnesota-Duluth (hockey).