In our 14th level party, our fighter/barbarian runs into 'only can miss on a 1' situations all the time. Between high levels, high str, rage, feats, and magic weapons there's a lot that's a threat to the party, but she can hit pretty easily. When my (late) bard threw out a +1 and extra attack from haste, +4 from inspire courage, and +3 from inspire greatness (and this was his normal strategy), it came up even more often. Our cleric keeps falling victim to failing saves that he can only fail on a natural 1 (though I think on the spell that killed him and my bard -- where I rolled a natural 2 -- he probably could have rolled a 5 and still died).
And occasionally we run into highly defensive and/or buffed up bad guys; until they're debuffed, it's sometimes the case that no one except the fighter/barbarian (and sometimes the soulknife) can hit the guy on less than a 20.