Some quick thoughts on a pair of rivalries I know fairly well:
Willamette/Linfield dates back to 1902, though it disappeared for the better part of the early 20th century when Linfield's Baptist leaders decided that football was too violent a sport for their school. Once it resumed, there were some serious off-field shenanigans. I once read an article - can't remember where offhand, but I could probably track it down - that at some point in the 1930s or 40s, a highly regarded football player from southern Oregon was recruited to play football for Linfield, but mistakenly got off the train in Salem. When he came to Willamette for help (the campus is across the street from Salem's train station) Bearcat coach Spec Keene instead gave him a uniform and got him to start practicing with Willamette's team. IIRC, after the Wildcats found out what happened, some Linfield players snuck down from McMinnville and brought him back to Linfield in the middle of the night. The player later became an All-American for the Wildcats.
More recently, I can give some on-field moments: then-Willamette coach Dan Hawkins rubbing some serious salt in Linfield's wounds by bringing Liz Heaston on to kick PATs in a 27-0 win in 1997. Linfield breaking Notre Dame's winning seasons streak in a come-from-behind win in McMinnville the next year (wildcat11's got video of that one). A 1-3 Willamette team upsetting the #12 Wildcats on a field goal with 4 seconds left in 2007 (I was there for that).
The lesser-known rivalry, probably because it's been so much less competitive, is Willamette's trophy game with Lewis & Clark: The Wagon Wheel game. Willamette's only lost the Wheel once in the last 20 or so years, but when they did lose it in 2000, the team spent the offseason rehearsing the ceremony they'd perform when they won it back the next year. From what Speckman tells me, it was a success. Now, with L&C on the rise, the Pioneers see the Wheel as a symbol for all their years of futility. I've been hearing rumors - not sure if they're offhand or not - that if/when they get it back, they plan to burn it. Which would really pour some gas on that rivalry.