For reasons of history, drama, number of classic match-ups - whatever qualifications you like.

Watched a documentary the other day about the rivalry between Alabama and Auburn university (American) football teams - sounds jokingly provincial, but you could not convince those fans that it wasn't the greatest rivalry in the history of sports. Is certainly a fun one, especially with this guy on the loose again: http://sports.yahoo.com/blogs/ncaaf-dr-saturday/auburn-tree-killer-harvey-updyke-released-prison-143354072.html

Other contenders?

Real Madrid / Barcelona
England / Australia (cricket)
Wales / England (rugby - if you're Welsh at least).
Ali / Frazier