Ok long post time!
I've lived amongst the Badgers for two years now & I'm still not sure I have a handle on this topic. They claim to hate everybody, so it's a tough job. I can't speak for the undergrads, who I spend next to zero time with, but I've put some effort into breaking down the Badger psyche based on my young alumni friends / fellow grad students. The best I can do is organize their opponents into tiers of hatred & discuss exactly why they despise each one.
Tier 1 - I'm going to drop MSU solidly into tier 1 after last season. Losing to Sparty on a final play hail mary drove the city of Madison into an alcoholic tailspin for at least two consecutive nights. That loss pretty much buried Wisconsin's national title hopes. When the Badgers realized they may very likely face MSU for a 2nd time in the B1G championship game, they could nearly taste the sweet blood of revenge between their sharper teeth. As a result, we got weeks of non-stop cursing directed towards the goons of East Lansing. That one really had time to simmer last season.
Wisconsin hates Ohio. They have a jealous rage towards both Ohio & Michigan, but I honestly believe they have less respect for Ohio (who can blame them?). You can buy t-shirts on State St. mocking tatgate & the Vest, which was surprisingly comforting to me. Wisconsin fans do have a sense of righteousness, as if doing things the right way makes them feel better about not historically achieving the level of success that Ohio has.
Michigan absolutely makes tier 1. They hate us for the typical reasons - we are arrogant & successful. I don't go out of my way to kick up dust because I like the Badgers, but when they inevitably give me shit for being from "mainland" Michigan (seriously, they are familiar with the UP but they can't figure out what the lower peninsula is meant to be called), I like to reinforce the stereotype by reminding them with facts & figures why we are better than them. It's not hard to do when you can cite 11 national titles to zero & call it a day. But honestly, I cheer right along with them for Bucky so long as it doesn't conflict with my Maize & Blue interests.
(Side note: You know that t-shirt about water covering 70% of the earth & Charles Woodson covering the rest? They have that here, but it's in green & yellow.)
Tier 2 - Nebraska earns high tier 2 honors as the new kid on the block with an ego problem. Badger fans everywhere delighted in welcoming Bo Pelini's squad to the B1G by taking them out back & thrashing them in a humbling massacre equal in magnitude to the one put on them in the Big House later on in the season. Badger fans have a lot of pride, & their blood boils when the opposition's talk reaches a certain level. Nebraska definitely reached that level before coming to Madison. That being said, the Friday night prior to the game was truly incredible as far as the sheer number of Cornhusker fans that invaded downtown & drank their asses off with the Sconnies. It was a pretty great night of posturing & predictions by both sides, so this one is a healthy part hype with a slightly smaller emphasis on hate.
Minnesota. They are supposed to be more hated than they are, but the rivalry has been too one-sided recently to really stir up those old feelings. A Badger fan will never miss the opportunity to smack talk the Gophers, but at this point it's kind of like going through the motions out of a sense of duty. The disdain is still there, but the Badgers don't feel threatened enough by the inferior mammals to the North to really embrace the dark side.
Tier 3 - Illinois gets the top of tier 3 because Wisconsin doesn't like that Illinois thinks they are such a great state. They think Chicago is overrated.
Tier 4 - Everyone else.
You'll notice that four out of the five teams comprising my first two tiers are actually not even in Wisconsin's division (the exception being Ohio) ... They do get the cross-divisional game with Minnesota every year I think, and both MSU & Nebraska are on the schedule for 2012.
So yeah, that's my best guess. But I'll bet if you ask another Badger, they might give you a totally different run-down. I suspect the Badger brain is 70% blind rage, 20% drunk, & 10% reason. So each individual fan could have their own unique set of grudges based on whatever seasons their brandy-pickled minds can remember, limited further by which of those seasons Wisconsin was actually good, & determined largely by whatever isolated instances triggered apoplectic fits of cheese-flinging & bouts of amusingly-accented shouting.