Until the BCS came about, there wasn't a National Championship game, so there's no absolute answer.
I assume you are talking about games that had we won, we'd have probably been #1 in at least one major poll, but not games like the Georgia Tech game where they won and got a share, but we had no chance.
Obviously the 5 championships count.
Also 2001, 1993, and 1983 for sure.
1981 possibly...I think the Sugar Bowl turned out in a way to give us a chance if we had beat Clemson, but there's no guarantee at all we'd have got.
1966 was like that too, 1 & 2 lost earlier in the day so had we beaten Alabama, we'd have probably taken it, I think. Both of those years are like how things fell our way in 1970.
There may have been another year or two where things possibly could've fallen into place, but didn't, so by game time we knew the championship wasn't on the line. I can't remember any like that for sure though. 1982 would've been a possibility since we only had 1 loss, but I think 1 & 2 were playing each other?
Looks like 10, unless anyone else can come up with anothe one.
