Erm, there probably is a big rivalry with Guatemala and Honduras, too, but the infamous Football War was fought between Honduras and El Salvador in 1969. That link already makes that clear enough, but here’s a short summary in wikipedia about the subject.
Depends what foot you kick with.
You always say your own team first.
One of the guys on ESPN’s Around the Horn that commented just today that this rivalry consists of two teams battling for second place in the NL Central. 
But at least they’re playing in the playoffs. Even if the major games have always gone NY’s way, the hatred reaches a level that I don’t think Cubs-Cards can touch. Cubs fans are basically nice people and Cards fans probably are too. This is the Midwest. Yankee and Sox fans are much more brash - what compares to rightfield in Yankee stadium? If I was a ballplayer I wouldn’t go out there. And unlike most of the other rivalries, this one is arguably at its peak now, with the amazing series last October (the fights and the super-dramatic Boone homer) and the arms race the two teams staged this offseason.
LA/Sacramento, maybe. I think Bulls/Knicks was a rivalry in the Jordan era. The Bulls always won, but the teams still geared up to play each other.
I agree about your NCAA picks.
I wasn’t going to bring the religious aspect into it. Alphebetically, we come first 
So, can I take it you follow the Cloven hooved Forces of Darkness from Mount Doom/ Ibrox?
Nurotik, your question is a great debate topic all of it’s self, that I would happily take part in some time.
I rank the Cardinals-Cubs ahead of the Yankees-Red Sox because to a certain extent I agree with the Yankee fans who compare the Yankees v. Red Sox to hammer vs. nail. Correct me if I’m wrong, but I can’t remember when the Red Sox ever beat the Yankees in a big game, as opposed to winning in May or winning 3 games in a best of 7 playoff matchup. While the fans of both NYY and BOS are certainly extremely passionate about baseball, the fact that some of them brandish weapons doesn’t mean that their passion runs deeper than those of Cardinal or Cub fans.
But at the end of the day I don’t have a dog in either fight. As a Cleveland Indian fan I’m jealous of everyone, excepting Tampa Bay.
English Football (these are games that you get hurt at - which is as good a benchmark as any):
Spurs vs Plumpstead Wanderers
Millwall v West Ham
Man Utd v Liverpool
Man Utd v Leeds
Man Utd V Man City
The rest of the country apart from those surrey tossers who make up their support V Man Utd
Stoke V Burnley (and pretty much anyone else)
(sort of English) Cardiff v Swansea
Sweaty Football:
Celtic v Huns
Hearts v Hibs
International football (from an english perspective):
Eng v Scots (more strongly felt north of hadrians wall)
Eng V Germany (the big one for most Englishmen)
Eng v Argentine (nb this predates the Falklands - although that didn’t help!)
Cricket:
Eng v Australia (although it would help if we could actually give them a game sometime soon)
But the only game in the World that I could see setting off a nuclear war (yes really) is:
India vs Pakistan.
Can any one else think of a game that could lead to a million deaths?
It’s the traditional rivalry with all that entails, but I believe the Oregon - Washington rivalry has become more heated of late. Much in the same way that Cal and Stanfurd are traditional rivals, but Cal fans loathe and despise USC with every fiber of their being.
Like it or not, if we’re talking about current NHL rivalries, while the games still generate a lot of interest and emotion, Montreal/Toronto has nothing on a lot of other pairings. Boston/Montreal is in the same situation.
For pure fan hatred, I’d have to say Islanders/Rangers is number one, even if the teams aren’t top contenders. Colorado/Detroit was very heated, but has cooled off a lot. If Claude Lemieux was still with Colorado though…
Toronto has three notable rivalries. Ottawa/Toronto would be number one, followed by Philadelphia/Toronto. The Senators, Flyers and Leafs are all contenders. Then there’s Buffalo/Toronto, but the Sabres are not contenders. (If they only played the Leafs, however, they might be.)
And then there’s Calgary/Edmonton. No matter how good or bad a season either team is having, their games are always heated.
So, the top three rivalries in the NHL today are - in no particular order - Islanders/Rangers, Ottawa/Toronto, and Calgary/Edmonton. (Philadelphia/Toronto, Colorado/Detroit, and Buffalo/Toronto would be the next three - again, in no particular order.)
Anyhoo…
International football rivalry
Seen from an English perspective: England-Germany.
What is it from the German perspective? When I lived in Germany, I mostly saw ze Germans baying for the blood of Holland… there was even a song for when Holland didn’t qualify for the World Cup!! “Ohne Holland gehen wir zum WM” or something to that effect. Maybe one of the German posters could chime in here?!
In Formula 1 of the olden days, Senna vs. Prost was brilliant.
Bears v. Packers
But again, when was the last time the Cards and Cubs played each other in a game that counts? Have they ever met in the playoffs?
No, that’s intended to show (in part) how much the players and ownership of the teams hate each other.
Ducks fans and Kings fans don’t like each other, but they are a rather small group compared to other sports fans in Southern California.
Southern California’s most successful team, the Lakers, is hated by pretty much everybody else in the country. The only team that Laker fans used to get really riled up about was the Celtics, but since they haven’t faced each other in the Finals for years, it’s not a big deal. Laker fans most likely hate Sacramento more than anyone else.
Giants fans hate the Dodgers far more than the other way around. The Dodgers and Angels are showing signs of a rivalry this year, mainly because the Angels are finally trying to market themselves alongside the Dodgers and advertising in L.A., and not just Orange County.
Yes, this rivalry exists and when the Netherlands didn’t qualify there was a huge amount of our trademark Schadenfreude. However I would say that the the rivalry with England is much more “serious”. The incident in 1966 only added to this. Nowadays the German Team isn’t what it used to be and losing against France, Italy or Brazil isn’t that much of tragedy anymore, but losing against England is not funny. OTOH beating England feels almost as good as a title.
A big German rivalry exists between Borussia Dortmund and Schalke 04.
Bayern München (Munich) is hated by almost anybody else, but the most clearly identifiable rivalry is the one with the other Munich Team TSV 1860 München.
Is that German for “neener neener, we made the World Cup and you didn’t…”
Let’s see…
Kentucky vs. Louisville (pretty much any sport)
Kentucky vs. Duke, UNC and Florida (basketball)
I’ll second Cards vs. Cubs. As a member of Cardinal Nation, I can only support the Cubs in 2 situations: 1) when a Cubs win helps the Cards and 2) in the unlikely event of a Cubs World Series win (because everyone will be celebrating if that happens.)
In NASCAR, I’d have to say Earnhardt Jr. vs. Kenseth is, based on their history in both Busch and Cup (Little E won 2 Busch titles, but Kenseth took RotY in Cup and was the 2003 Cup Champion).
I don’t know about that. Cub fans can be pretty insufferable, and the more non-Cub fans are exposed to actual Cub fans, the less popular the Cubs will become naionally. Cub fans and TV executives just kind of assume that other baseball fans like the Cubs when it isn’t necessarily so. Baseball fans like their own teams, hate their rivals and generally don’t give a darn about the rest of the teams. WGN has made the Cubs popular in the hinterlands where the people don’t have major league teams of their own to obsess over, and there are enough Chicago expatriates around to seed Cubfanness around the country, but where there is already a team the Cubs aren’t too many people’s favorite team.
Case in point. My brother-in-law is from a little town in Wisconsin on the border between being a Cub fan and a Brewers fan. He became a Cubs fan. Last September he and my sister came to visit back here in Cleveland, and he, having been indoctrinated to Cub-fan-ness, was amazed to discover that very few in northern Ohio gave a damn about the Cubs. He somehow thought the Cubs playoff chase would be the lead story on the local Cleveland TV news. He was wrong of course, (because sadly enough, the Browns quarterback controversy was the lead story on Cleveland local tv news.)
This just bears repeating again. This is a TRUE RIVALRY that happens every year in, and year out, regardless of who’s a contender and/or non-contender. Spend a week or two in California, and you’ll understand what true rivalry is. This rivalry is more than just sports.
…and regardless of what home team that the visiting Lakers or Dodgers play, how can you not ignore the crowd chanting “Beat L.A.!”? Our fans get bashed all the time for not being there to support their team (which is horseshit BTW - all fans are like that), especially when L.A. is a huge conglomeration of transplanted fans from the rest of the country as well as world.
I thought it was
Microsoft - Customers
I would suggest that England-France has just jumped–if only temporarily–to the top of the international football rivalries.