Washington and Washington State play for the Apple Cup, Arizona and Arizona State play for the Territorial Cup and Mississippi and Mississippi battle for the Golden Egg.
But Oregon and Oregon State only play for bragging rights and maybe a trip to El Paso for a bowl game.
It wasn't always this way.
In the fall of 1959, Willard Thompson, the University of Oregon's director of public service, selected Warren Spady from among several art students to sculpt a wooden platypus that would be given to the winner of the Civil War.
With only a month before that year's game, Spady got a block of maple and did his best. When the game arrived, Spady thought the platypus feet still needed a little more work. He was told not to worry because the 15th-ranked Ducks would certainly trounce the 2-7 Beavers. With the trophy safely in Eugene, he could add the finishing touches.
But Oregon State shocked the Ducks and their fans ran off with the unfinished trophy.
Though the 1960 game ended in a tie, the trophy somehow managed to get back to Eugene. It was supposedly stolen by fraternity brothers from a trophy case at Oregon State's Gill Coliseum, said Spady, who's now 71 and living in Redmond.
The Beavers won the 1961 tilt and former UO vice president Dan Williams, who was student body president at the time, remembers delivering the platypus to Oregon State's student body president.
Somehow it ended up in the hands of Oregon's water polo team in the mid-1960s and the platypus was no longer part of the Civil War.
In 2004, Oregonian sports columnist John Canzano wrote that the Civil War really should have a trophy. Spady e-mailed Canzano to say it does, or at least it did. Williams also read the column. Curious, he launched a search party.
Athletic department equipment personnel later found it in storage at the Moshofsky Center by Autzen Stadium. Spady visited Eugene to identify the trophy, and Williams delivered it to the UO alumni office earlier this year.
The alumni association is trying to resurrect the awarding of the platypus trophy. An on-field presentation after this week's game seems unlikely, but it could happen in the years to come.
"It seems appropriate that two teams who are seen across the nation as having two of the sillier mascots would have an appropriately silly trophy," said Kevin Miller, communications director for the alumni association.
Civil War's Platypus trophy lost, then found