UW will always be #1 that should be fairly clear.
Okay now the other 4 that is tricky.
Now what exactly constitutes a rivalry? Is it mutual dislike, is it just something we care about? Really sort of depends on your views.
Now the #2 team I do think is Gonzaga because they are in state canceled our home series and act like they are “too good” to play us. Rivalries usually need reciprocal dislike and Gonzaga looks down on us we don’t like their uppity attitude close proximity in state yeah it’s a rivalry but it is just in Basketball.
Now on to #3 - I would have to say Idaho because of Proximity / history but because of Idaho’s poor athletics it just isn’t fun and really doesn’t have any bitterness from the past competition. It’s like a neighborhood friendly that we feel sorry for these days. I really do with they were strong athletically it would be great for the region but alas this is like a zombie rivalry...it’s dead but it could still be alive too.
#4 I would have to say Boise. Because Boise is a team that WSU fans don’t like because of their sucesss, they are nearby and remote and they are obnoxious. They also like to talk trash and beat teams in bigger/more prestigious conferences so they sort of have an chip on their shoulder attitude and that clashes nicely with our jealous for a PNW rural area proximity.
#5 May surprise some people but I am going to say USC. Now from the other perspective of USC this most certainly is not a "rivalry". UCLA is a rival, Notre Dame, Stanford possibly but not WSU, but I will explain why USC is the hidden rival for WSU.
WSU and USC are about as polar opposites as can be.
USC is a wealthy private school in a massively population center on the coast of the country in sunny warm breezy climate.
WSU is a modestly small public school in a rural and remote part of the country in a cold part of the country
Everything USC is WSU is the exact opposite, and so beating USC not only is a feat of accomplishment for WSU that it loves, but also when it does happen USC is incredibly offended. Furious, and so to me in an observational standpoint USC/WSU is the hidden rivalry that people don't realize exists. It's the classic David vs Goliath, Rich vs Poor, Small town vs Big City, Cold Rural Hills vs Warm Ocean Breeze, Fast Life vs Slower Pace juxtaposition as you can get.
And to show that the game does have ramifications because I think rivalry games have to "mean something" to the programs.
When WSU beat Kiffin in the Coliseum he was fired basically after the next week.
When WSU beat USC last year a USC player basically attacked a WSU fan celebrating.
There is a bitterness that USC has when losing to WSU that other teams don't have, and there is a glee and jubilation exhibited from WSU when it beats USC that usually is only seen when we beat UW. It's there, but rarely talked or focused on.
Oregon/Oregon State are well their own rivalry and while close we have more in common with OSU than just about anybody and kind of root for each other. Oregon we just sort of see as Phil Knights marketing program, and while beating them is wonderful, it just doesn't have the emotional magic that I think is necessary for a rivalry game.
Utah/Colorado/Stanford/Arizona/ASU/Cal - are just there.
But UW/Idaho (at least in the past)/Boise/Gonzaga/USC all really mean something. There is bitterness, resentfulness, close proximity (aside from USC but it is king of juxtaposition) They all bring something to the game on an emotional level.
Beating UW - Obviously in state rivalry bragging rights
Beating Idaho - Neighborly bragging rights
Gonzaga - Neighborly bragging rights
Boise State - Chip on their shoulder vs Jealousy Close Proximity rights
USC - The grand juxtopistion of location, culture, resources