Watched this earlier about the Rangers / Celtic rivalry - I don't think it's the most intense in football, but it's pretty big. They talk about a 15 year old Celtic fan having his throat cut simply because he was a Celtic fan, and the history of violence between the two teams.
I remember when Luis Figo moved to Madrid from Barcelona he had bottles, coins, golf balls and pig's head thrown at him when he went to take corners and throw-ins. The Fenerbahce vs Galatasaray rivalry is pretty intense too. I think football's rivalries are easily bigger and more intense than the rivalries in any other sport.
Came here to say the Old Firm, but that's the one I've had the most exposure to. Got to say most people I know aren't like that (it's good for a banter but none of that sectarian nonsense) but I have spoken to some right bastards on both sides.