This one is pretty recent ... but the Deathclaws from Fallout New Vegas.
I'm a low-level stealther. I'm walking normally, I see something in the distance I think is another damn rock. Then it moves.
I hit that L3 button and sit there frozen. Slowly, I identify the legs and tail and realize what it is. I know I'm too weak to kill it, but I can't help thinking Maybe if I can just sneak up on it with my machete ... I spend the next ten minutes inching toward it as slowly as I can, carefully flanking it, knowing that it could turn around suddenly and eat my face.
Suddenly the word on the top of the screen starts flashing DANGER. I'm too confused to react - the thing's not even looking at me! It hasn't even moved in fifteen minut-
A couple of other Deathclaws have snuck up behind me and killed me instantly, presumably with a bite to the neck. As a final insult, with the camera slowly panning away from my dead body, the Deathclaw I was stalking hasn't even turned around.
Oh, and the Cazadors. And the Radscorpions. And the Centaurs. And - fuck it, every single thing in the Mojave is trying to kill me!