Back when the SEC's upcoming requirement of playing at least one major conference opponent in the non-conference came about, I looked at how often teams failed to schedule such a game since 2006. It turned out that it wasn't terribly often.
Something I meant to do at the time but that got lost in the shuffle was seeing when the last time each SEC team failed to schedule a major team in the non-conference. I decided to go back to 1933, the first year that SEC football existed. Four current teams weren't in the SEC back then, of course, but I looked at them anyway.
Doing this task is not easy once you get past a couple of decades ago. South Carolina was an independent for a while, so every game it scheduled from 1972-91 was technically a non-conference game (pencil in a N/A for that school for those years, basically). But there's more than just that.
When were the service academies no longer considered "major"? I'm not 100% sure, but I think it was in the mid to late '60s. When did Miami and FSU become worthy of "major" designation as independents? I'm going with 1944 for the former, based on scheduling, and 1960 for the latter, based on history. What about Southern Conference schools from way back? If a team would become a founding member of the ACC in 1953, then I considered it "major". What about the AAC last year? If it formerly was a Big East school, then it counted as "major" for that season.
Anyway, these considerations are only relevant for a couple of schools. For most, you don't have to go back that far.
Nine of the conference's 14 schools have skipped or otherwise missed out on a major non-conference opponent since the years no longer began with a one.
- Texas A&M, 2013: Rice, Sam Houston State, SMU, UTEP
- Mississippi State, 2012: Jackson State, Troy, South Alabama, Middle Tennessee
- Ole Miss, 2011: BYU, Southern Illinois, Fresno State, Louisiana Tech
- LSU, 2008: Appalachian State, North Texas, Tulane, Troy
- Arkansas, 2007: Troy, North Texas, UT-Chattanooga, FIU
- Alabama, 2005: Middle Tennessee, Southern Miss, Utah State
- Missouri, 2005: Arkansas State, New Mexico, Troy
- Auburn 2004: UL-Monroe, The Citadel, Louisiana Tech
- Tennessee, 2000: Southern Miss, UL-Monroe, Memphis
A note on Ole Miss: even though the SEC and ACC won't consider BYU fit for fulfilling the major non-conference opponent requirement, some people do consider it worthy of the distinction anyway. If you are one of those people, for you, the Rebels' date moves back one year to 2010 and its non-conference slate of Jacksonville State, Tulane, Fresno, and UL-Lafayette.
The 2005 date for Alabama goes a long way in explaining how Mike Shula was able to win 10 games that one time.
The 2004 non-conference slate for Auburn was a subject of some controversy that year, if I remember correctly.
For the younger fans out there, college football adopted a 12-game schedule provisionally in 2002-03 and then permanently in 2006. That is why the number of non-conference opponents changes.
More recent beyond that
Two more teams have gone longer with their streaks of having a major non-conference opponent but who still haven't hit 30 years or more.
- Vanderbilt, 1997: North Texas, TCU, Northern Illinois
- Kentucky, 1986: Rutgers, Kent State, Cincinnati
TCU was not a major conference team in 1997, so it doesn't count. It was 1-10 that year, so it doesn't get a pass for team quality on top of its former SWC pedigree either.
Rutgers was still an independent in 1986, and it was an awful one at that. I am not counting it as major before it joined the Big East in 1991.
Going way back
Two teams have held out for a lot longer of a period of time since the last time they failed to get a major non-conference opponent.
- South Carolina, 1943: Newberry, Fort Benning, Presbyterian, Charleston Coast Guard
- Georgia, 1942: Jacksonville Naval Air Station, Furman, Cincinnati, UT-Chattanooga
South Carolina is where the service academy question comes into play. Its only major non-conference opponent in 1955 was Navy, and its only in 1954 was Army. I believe they were still major at the time, Navy especially as it would finish the 1962 season ranked No. 2 in both polls. Maybe someone can shed some light on this in the comments.
Both of these years for these teams came during World War II, a time when many teams didn't even play for one or more years. You might consider giving them a pass for that reason. I am disinclined to do so simply because they didn't play each other as they did from 1937-41.
If you want to give them a pass on these, then South Carolina's date goes back to 1934 (Erskine, the Citadel, Villanova, Furman) and Georgia makes it all the way back to 1933 unscathed as long as you consider the SWC's Rice as "major" in 1936.
Comfortably in the "never" zone
Only one team is left if you're counting along at home: Florida. The SEC team that gets the most grief about its non-conference scheduling due to its disinclination to play non-conference series with teams other than Florida State and Miami (FL) has unambiguously not missed an opportunity to play a major team in non-conference play since the SEC itself began.
The series with Miami alone covers most of the program's history since 1933. From 1944 (when I'm counting Miami as "major") to 1987, that series by itself takes care of things. The rivalry with Florida State takes over from there although it overlaps quite a bit, stretching back even before the 1960 mark when I'm considering FSU "major". From 1933-42 (the school had no '43 team due to the war), an annual series with Maryland actually covers the non-conference requirement, though there were games with teams like South Carolina, UNC, NC State, and Texas in there.
So what was the point of all this? It's the offseason, which is the time to look these things up, and to have it as a reference. Of course, it's going to be out of date pretty soon. Four schools do not have a major conference opponent lined up this fall: Ole Miss, Mississippi State, Texas A&M, and Vanderbilt. The Rebels get some credit though for having Boise State, which was better than the average major conference team when the game was scheduled in 2010.