Besides the obvious "first 5 minutes of the game, lose to a mega boss during the tutorial" kind of encounters.
So I was playing FFXIII-2 the other day, and, at some point halfway through the game, you come across this big antagonist guy. Long story short, you get to fight him, and I beat him in about a minute with little to no effort.
But he's the big bad strong guy, and so the game promptly played the typical cutscene of my characters panting in the ground as he stood tall and mighty.
Every time this happens, I can't help but wonder how much of an impact it would have if I were forced to lose in these kinds of situations. I don't think there's a better way to make you fear an enemy of any kind than to have it beat you up. What are some examples where this is actually what happens through gameplay?