And by “legitimate fan” I mean a team you root for come hell or high water, win or lose, good season or bad.
Mine are (in order of fandom)
Auburn
Vanderbilt
Tennessee
Middle Tennessee
Samford (formerly Howard College)
The primary reasons for these would be family ties.
After those I have other preferences but nothing in the “legitimate fan” zone.
If you root for 3 teams in the same conference (Auburn, Vandy, Tennessee) it doesn’t sound too legitimate to me. 
I root for, in order of preference:
Notre Dame (Alum & subway alum)
Kent State (Alum)
Ohio State (local area big school team)
If they’re playing each other I’m a fan in descending order on that list.
As far as that goes, I’m basically an SEC fan, but there are teams in the conference I love seeing get beat. So there’s also that…
LSU, of course, my alma mater. But they’re always an undisciplined badly-coached team who loses by stupid mistakes. I hate Notre Dame, sick of having them shoved down my throat by the major networks, they’re the New York Yankees of football.
As a kid, I always rooted for UCLA to beat USC, but they never did. Always root for an SEC team (or anybody else) to beat a Big Ten team, especially Michigan, MSU or Ohio State.
UMass
Ohio State
East Carolina
All of them family connections. None is my alma mater, which barely even has a team.
Elvis, where you go?
Until the Sandusky scandal, I was a lifelong Penn St fan. Haven’t had it in me to root for them.
I went to MIT, which, at the time, had not lost a game in 70-odd years :). They’re now in one of the smallest Div III conferences in existence. The 2 or 3 frats who had a bunch of jocks in IM’s became the varsity residences instead. One of my masters degrees was online from a big-name school that I’ve never actually visited, but sends me fundraising letters all the time anyway. The other was for a school with no team, in a major that used to be their entire existence but was canceled right after I got the diploma.
I’m from Columbus, so Ohio State is a permanent condition. My daughter went to UMass, played in the band, had a great time, so did we going to all the games and band shows, and I love the place. Much of my wife’s family is in Greenville NC, where my BIL teaches at ECU, so I’m fond of them too.
Pecking order:
Kansas State (alum)
Auburn (alum)
what a week for me
My college didn’t have a team. My wife, however, is a legitimate fan of Iowa and i have become one by proxy. I don’t really care about any other teams, but do like it when Auburn or any Texas team looses.
Chingon: on the rare chance they play each other, how would you root? Personally, I’d root for K-State, for Chamberlain reasons. (“Nobody roots for Goliath”)
LSU, my alma mater.
They play this Thursday night. No question I will root for KSU.
Irony! 
Is it “Chamberlain” reasons guiding your rooting?
University of California (alumnus)
Nope, born in Kansas, parents went to KSU, siblings went to KSU, I have rooted for KSU since I could root for any team.
I could also mention that my mother worked for many years in a life-insurance business owned by a former OSU basketball player, who brought a lot of Buckeye athletes in to sell them policies. They never had a more loyal fan, even though she didn’t go there. But, along the way, she learned to hate Michigan State (not Michigan though), so I kinda do too. 
Texas A&M, my alma mater.
I also half-assedly follow University of Texas, because my father-in-law is an alum, and we talk football fairly often.
I keep tabs on the rest of the SEC, just to have an idea of who A&M is going to play, but I don’t usually watch any one team’s games or anything like that.
Which one?
I went to UCLA, so that’s my team. My dad went to Cal, though, and I grew up attending Cal games, so I still like for them to do well.
Magnus-Did you rib your dad when Cal played UCLA.
Ohio State.
I am from Ohio, and therefore cursed.