According to Merriam-Webster's dictionary, the first known use of the word rivalry occurred in 1598. The giants and Lilliputians were a bigger deal then than the Broncos and New England Patriots.
At its essence, sports are about competition, about keeping score. There's no recipe for a great rivalary. And it doesn't have to involve teams. In the AFC championship game, the best rivalry is arguably not Manning vs. Tom Brady. It's The Brain vs. The Machine. Manning against Belichick.
"There is not a player off my team I have more respect for than Peyton," Belichick said.