Despite what Saturday morning cartoons and your elementary guidance counselor may have told you, you are not unique and there is probably someone out there who is a lot like you in almost every way and the same can be said for college football program. As diverse as the geography, success and history of the Pac-12 conference is, I would argue that pretty much every team in the conference has at least a fairly close doppelganger that plays in another conference.
Washington = Tennessee
Both of these programs have unique game-day experiences that involve bodies of water and historical stadiums. They both have had lots of success in their past and some national championships, though only one in the modern era and not as many as the best school in their conference. They have both struggled through much of the 2000s and gone through a number of coaches and have to deal with having a good home state for recruiting, but not a great one. Also, both teams' mascots are dogs.
Washington State = Colorado State
Aside from the states of Washington and Colorado being very similar, both of these teams have seen success in the past 25 years under longtime coaches (Mike Price and Sonny Lubick), but have been unable to replicate it since they moved on. A lot of both the Cougars and the Rams' identity also actually ties into their rival and how often they are able to upset them, which is more frequent than one might think. Also, while Fort Collins certainly isn't as small or remote as Pullman, both are a ways away from the population hub of their states and very far culturally from the home cities of their rivals.
Oregon = Nebraska
Okay, 90s Nebraska more specifically. Geographically and looking at population statistics, the states of Oregon and Nebraska are very odd places to have powerhouse football programs, but both adopted unique offenses that when they are run effectively, are downright nearly impossible to stop. Both programs also used their success to recruit well nationally and have intense fan bases that are obsessed with their teams.
Oregon State = Kansas State
State schools in lightly populated states that have been turned into good programs by highly respected, veteran coaches that get the most they can out of the limited talent that they have.
Cal = Baylor
Despite being in very fertile grounds for producing college football players, both schools were more focused on academics until just recently when they started finding renewed success on the football field, harkening back to their better years prior to the modern era of college football. While both schools have had success, they haven't quite been able to outduel the elite powers in their conferences. Also, both are Bears.
Stanford = Far less prestigious Notre Dame
It is very hard to find one for Stanford though as they are a bit better at football than the schools that are most similar to them (Schools in major conferences with superb academics) like Northwestern, Vanderbilt and Duke. Clearly, they aren't anywhere in the stratosphere as their rival Notre Dame in terms of success, but they are a very old school, highly academic school that still produces big time athletics.
UCLA = Auburn
Yes, they are both very good programs, but it just never seems to measure up to that of their cross-town/state rivals and they seem to really lack consistency despite producing a number of great players. Culturally, the two programs probably couldn't be more different, but on the field, they a number of similarities, though many are actually tied into their rivals.
USC = Texas
Both are in the greatest college football recruiting states in the nation and both rule the roost. Both schools produce great running backs and have too many accomplishments to even try to list, especially national championships. They also both know semi-down years though, especially right now, which should seemingly never happen since they are always loaded with so much talent.
Arizona = North Carolina
Two schools that are very good at basketball but are only moderately good at football. See also - Kansas, Kentucky and Indiana.
Arizona State = Michigan State
Another tough one, but both schools have a reputation for partying and produce a good amount of players for only being above average programs. Also, I think people don't realize that Arizona State was really good in the 80s and people also don't realize that Michigan State was really good in the 50s and 60s.
Utah = Nevada & Boise State mixed together
Utah is maybe the hardest of any to peg as they are kind of tweener program that isn't a mid-major, but has only been in a BCS conference for a couple of years. I would say that like the Wolfpack, they are a mountain region state school that has had some inconsistent success, but are like Boise State, in that they have had a couple of outstanding, undefeated years, though they haven't had the sustained success of the Broncos.
Colorado = Boston College
Both of these schools have had some great success in recent history, but have also really been mired in tough years despite sporadically producing NFL players. Also, both teams are in markets that are much more interested in their professional football team that makes it tough for them to get much buzz going.