I know Boise St has done it multiple times. 2 or 3 at least. And they usually win when they get there.
Utah did it once, and spanked their opponent, before joining the P12.
TCU did it, maybe a couple of times, before joining the B12.
Hawaii did it once and got embarrassed in their BCS bowl game.
Didn't Northern Iowa or Northern Illinois do it a few years back?

Any others?

And BYU has done it...never. They won the "mythical national championship" in 1984 based on an unbeaten regular season where everyone else ahead of them in the polls kept losing, and then they beat Michigan in the Holiday Bowl. They've come close a few times, but they always seem to lose that one game that kills their chances. Or they start off the season hot, and then stumble unexpectedly against someone they should beat. Fans year for a breakthrough. BSU, Utah, TCU, Hawaii, etc., they've had those breakthroughs. BYU hasn't.