“The Red River Rivalry” Texas Longhorns vs. Oklahoma Sooners.
I’ll pass on all the teams that play “The Game”.
El Clasico: Real Madrid vs Barcelona, coming up this weekend
The Iron Bowl: Alabama vs Auburn
The Egg Bowl: Mississippi State vs Ole MIss
Oregon v. Oregon State: The Civil War
Kansas v. Missouri: Border War
The Border War: Missouri v. kansas
Probably one of the most hate filled rivalries between two fan bases. Schools are active participants as well, the kansas football team wear red socks for games in Missouri the way guerrilla fighters did during the Civil War. Missouri fans are known to fly the black “Quantrill’s Raiders” flag, and wear tee shirts depicting the burning of Lawrence with “Scoreboard” printed on it.
eta: Damn it, Munch.
You must be a youngster; it was called the Red River Shootout until that became non-PC.
Cal and Stanford play The Big Game, if that passes your criteria. 
BYU - Utah: The Holy War
Florida - Georgia: The World’s Largest Outdoor Cocktail Party
Pitt - West Virginia: The Backyard Brawl
Boston College v. Notre Dame-Holy War
Not unless that’s strictly a BC thing. I’ve never heard anyone in South Bend ever say that.
Indiana and Purdue play for the Old Oaken Bucket.
The phrase “Clean, Old-Fashioned Hate” is applied to both Georgia-Florida and Georgia-Georgia Tech, although it’s less the game per se, and more the rivalry in general.
Georgia-Auburn is “The Deep South’s Oldest Rivalry”, and North Carolina-Virginia “The South’s Oldest Rivalry”. Both nicknames are perfectly accurate and utterly boring.
Wahington v. Washington St. is The Apple Cup.
In general, in Spain rivalry games are called “derbies”. As well as el clásico and off the top of my head, they include el derby sevillano (Sevilla/Betis), el derby vasco (Real/Bilbao), el catalán (Espanyol/Barça) or el madrileño (Real Madrid/Atlético).
The Alabama vs. Auburn game was called The Iron Bowl because it was played in Birmingham for many years and referred to the steel industry in Birmingham. The game hasn’t been played in Birmingham since 1998, and now takes place on the Alabama and Auburn campuses in Tuscaloosa and Auburn. We still call it the Iron Bowl, though. This concludes your Iron Bowl history lesson. 
Roll Tide!
I read Phil Ball’s (one of 2 weekly La Liga columnists on soccernet.com) column yesterday. He lives in San Sebastian, so he was writing about the Real Sociodad-Athletic match this past weekend, and he pointed out what I found fascinating: for matches at both Real and Athletic, the fans aren’t separated from each other as is so often the case in Europe, and they party together both before and after the match. If I ever get to Spain, I may have to make that my match of choice rather than give an arm and a leg to see Barca and Madrid.
“Derby” for rivalries, commonly local, is an English phrase that dates back to the eighteenth century and was in common usage by the early nineteenth century.
The majority of matches in Spain don’t have the fans separated, although you may want to avoid getting a seat directly behind a goal: for those teams that have “nasty” fan groups, these tend to prefer that area (nasty with commas because some are truly nasty but others are just loud). The only time I’ve been in a pro match it was an Espanyol-Osasuna; since it was in Barcelona, most people were Espanyol fans. The only person who misbehaved was my gramps; there was a little kid who’d refused to let his uncle buy him Espanyol parafernalia, liking Osasuna’s colors better. When Osasuna had a good move, the people around us congratulated me and joked with the kid’s uncle that “hey, maybe the kid chose right!”; when Espanyol did, I congratulated them. It’s what going to the game is about, for most people - enjoying the show in good comradeship, not behaving like Gramps and yelling “castrate him!” every time that Osasuna central defense Pepín stole a ball from an Espanyol forward…
Amanset, I know it’s from English, but last time I checked, English wasn’t one of Spain’s usual languages - derby is one of many English terms which are used in soccer and which surprise us when found in another context (“Ascot Derby? Which teams play? I didn’t know there was a big team called Ascot!” “No, it’s horses” “UH?”). One of my American coworkers was very surprised to see a bar called “Crack”, another soccer term from English (from “crack shot”, a very good forward); also míster for the coach, and of course the names of many plays (penalti, córner).
It is used internationally, especially in terms of football. Sweden, where I live and also a country that doesn’t have English as a “usual language”, uses “Derby”.
Basically, the use of "Derby"in Spain isn’t anywhere near as unusual or surprising as you seem to think it is.
Sweden: Ingen bäst i klassiskt derby
France: http://www.lemonde.fr/sport/article/2012/03/03/ligue-1-montpellier-sous-pression-lille-en-chasse_1651256_3242.html?xtmc=derby&xtcr=29 (Derby Breton)
Germany: 2.Liga: Fans feiern Fiel | Sport | BILD.de
Italy: Il derby non fa il pieno
Netherlands: Sport | Het laatste nieuws uit Nederland lees je op Telegraaf.nl
Portugal: http://www.abola.pt/nnh/ver.aspx?id=355195
OK, so we’re talking at cross-purposes here. All I was saying is that in Spain they’re called derbies in general (also other names but that’s mostly for variety during newscasts) and giving some specific names for a handful of them.
I don’t think it’s unusual or surprising given how many soccer terms used in Spain’s languages are from English and how many are international, what miffed me is that you found the need to point out that it’s from English.
And in other countries (hell, I’d say the majority) they are also called derbies in general.
I replied because - and maybe you don’t realise this due to not being a native English speaker - that the way you presented it came across as you thinking that “Derby” was a local term rather than one that was internationally used and known.
Sorry if it came that way but no, I could never make such a mistake. All I was saying is that it’s the term normally used in Spain - I never said anything about other countries, nor intended to imply anything about other countries.