This is looking at the stakes of a game going into the game and is independent of how the game turned out (win or lose or future importance) - emphasis is just on how big the game was going into it.

For example, BYU only lost 1 game in 1980, to New Mexico in the opener.  In retrospect, that game was huge, but at the time there was no real hype or excitement about two unranked teams meeting.  For a game to be a huge game and involve an unranked team, there needs to be some special circumstances

For BYU (in chronological order)

1. 1974 Fiesta Bowl #17 BYU vs unranked 6-5 Oklahoma St: This was the first year BYU had been ranked and was an opportunity to finish a season ranked for the first time...but lost and had to wait until 1977
2. 1977 #13 BYU vs #17 Arizona St: BYU had never before finished a season ranked, they'd been up to #13 earlier before losing to unranked Oregon St, but this was a matchup of Top 20 teams. BYU loss (but still finished ranked)
3. 1979 Holiday Bowl #9 BYU vs unranked 7-4 Indiana: Not a great opponent, but was a chance for BYU to finish their first undefeated season and achieve a first-ever top ten season. BYU loss  
4. 1980 Holiday Bowl #14 BYU vs #19 SMU: Huge game (and an undeniably amazing actual game), but hurt by the limited larger importance of the game. Still, one of the first highly ranked BYU matchups shown to a wider audience. BYU win
5. 1984 Unranked BYU vs #3 Pitt: Coming off a top 10 finish (but unranked), BYU squared off with the #3 overall team.  Pitt ended up being a bad team that year, but at the time it was a huge game. BYU's lack of ranking hurts, but is largely made up for by the previous season's success. Hard to assess this one fairly without getting into retrospect, both for what it meant for BYU and how bad Pitt ended up being. BYU win
6. 1984 Holiday Bowl - #1 BYU vs unranked 6-5 Michigan: hype/excitement suffers a tiny bit because the opponent was underwhelming (the 6-5 even oversells how good they are, they'd gone 3-4 after losing their star QB to injury).  Washington (and others) had the opportunity to play BYU and had declined due to the lower bowl payout.  Plus, given the system, there was some uncertainty that Oklahoma might pass BYU if they beat Washington.  Still, cemented the only championship in state history and was at least likely to bring a national championship with a win.  Obviously a BYU win and probably the biggest single game in BYU history
7. 1985 #8 BYU vs #20 UCLA:  As defending national champs, their first real test of the year against a quality ranked team. BYU loss
8. 1985 #16 BYU vs #4 Air Force:  Had the potential to be bigger with BYU as defending national champs and Air Force a top 5 team...but BYU had already dropped a couple games that year. BYU win
9. 1986 #11 BYU vs #7 Washington: Top 11 matchup with BYU coming off a 13-0 and 11-3 season. BYU loss
10. 1990 #16 BYU vs #1 Miami: BYU entered the season with high expectations, ranked #16 off the bat and welcomed defending national champion Miami to Provo in a huge clash. BYU win
11. 1990 #4 BYU vs unranked 6-5 Hawaii: Chance to finish the season as a top 5 team and potentially get a better bowl invite.  Loses value because BYU already had one loss and would have had a hard time getting up higher than #4 anyway and also because the WAC contract with the Holiday Bowl likely would have kept even a Top 5 BYU team there.
12. 1991 #19 BYU vs #1 Florida St: Similar to the game against Miami a year earlier, playing the #1 team in the country while highly ranked...this one isn't remembered as fondly. BYU loss
13. 1996 WAC Championship #6 BYU vs #20 Wyoming: Overshadowed by this season's Cotton Bowl win against Kansas St, was nonetheless a huge game as it helped BYU get to the much bigger stage and retain their high ranking. Very close game, won by BYU in OT
14. 1996 Cotton Bowl #5 BYU vs #14 Kansas St: High profile game against a marquee opponent with BYU holding the highest rank since the 1990 loss to Hawaii.  BYU win
15. 1997 #19 BYU vs #4 Washington: Coming off a top-5 season, BYU opened ranked against a top-5 Washington team.  It was an ugly BYU loss and a precursor to a 6-5 season, but was a big game at the time.
16. 2001 #9 BYU vs unranked 8-3 Hawaii: Huge implications here as it would have capped off an unbeaten regular season for BYU and given a strong argument as a BCS buster (or controversy if not selected).  Unfortunately ended up as a (very ugly) BYU loss.
17. 2008 #16 BYU vs #8 Utah: Probably the biggest game in the BYU/Utah rivalry (at least the best combined ranking), and Utah needed this win to keep BCS busting hopes alive. BYU loss
18. 2009 #16 BYU vs #10 TCU: BYU already had one loss, but was ranked right behind TCU (who ended up as a BCS buster that season) in a matchup that determined the conference and may have given BYU a chance to BCS bust if they'd won. BYU Loss.
19. 2015 #19 BYU vs #10 UCLA: BYU's first (and, until 2018, only) ranked-on-ranked matchup in the Independence era.  BYU loss
20. 2018 #20 BYU vs #11 Washington: The second ranked-on-ranked matchup for BYU in Independence.
21. 2020 #9 BYU vs #21 Boise St: After going undefeated against a weak opponent slate, BYU needed a marquee game to show they were for real.  Enter #21 Boise St for the 3rd ranked-on-ranked in Independence.  BYU won and won big
22. 2020 #13 BYU vs #18 Coastal Carolina: Even after beating Boise St, it was clear BYU would have to do a bit more to make an NY6.  Enter #18 CCU (on short notice) as the 4th ranked-on-ranked matchup in Independence.  This game got a LOT of hype, but unfortunately the result wasn't as good as the Boise St game a month earlier.  BYU loss
23. 2021 #10 BYU vs unranked 2-3 Boise St: Really, not fair to list this one as Boise St wasn't considered a great team this year and maybe should be replaced by the Arizona St game that same year (the only Independence ranked-on-ranked matchup not on this list). That said, BYU was a Top 10, undefeated team and Boise St had become a strong secondary rival.  If BYU had won this, the game the next week against Baylor would have been massive, but this was a BYU loss.
24. 2022 #21 BYU vs #9 Baylor: Coming off two excellent seasons, BYU had high expectations and squared off with the defending Big 12 champ early with both teams undefeated.  A classic game and a BYU win.
25. 2022 #12 BYU vs #25 Oregon: After beating Baylor, BYU's season looked destined for greatness.  With a #12 ranking (higher than BYU had been this early in the season within the last decade) and matched up against a ranked opponent, the sky was the limit.  Unfortunately, a BYU loss derailed that.