As intriguing as many find the upcoming world championship match between Viswanathan Anand and Magnus Carlsen, there is as yet no rivalry in chess history that compares with that between Garry Kasparov and Anatoly Karpov. They played five world championship matches in a six-year period, comprising 144 games in total (no wimpy 12-game matches for those two), and in all of them the outcome was unclear until very near or even at the very end.
Here is a video compiling both photos and footage of their rivalry from a simul battle in the mid-70s through their rapid and blitz match in 2009. A remarkable highlight to me is the footage of the end of the Seville match in 1987, which must have been one of the most shattering events of Karpov's career - if not his life. To look at Karpov (at the 9:00 mark; see the next 75 seconds or so as well) when he resigns the 24th game is to be amazed. Just to judge by outward appearances, he looks no more disappointed than many of us would be after losing a game at our local club. I've been unhappier after losing blitz games than he seems to be. That kind of remarkable composure probably helped him a great deal in his career.