Well, when I first encountered the Big Daddies in Bioshock, I was terrified of them...especially when I didn't have very good power ups and weapons. However, they do pretty much leave you alone unless you pick a fight with them, but I still personally wouldn't want to encounter one in a dark alley somewhere. I would hate to be at the business end of their arm-drill things...
I hate Big Boos in Super Mario World... Can't do anything against them except run away. Well, when you look at them, they get shy and cover their faces, which is kind of adorable. :3 EDIT:: OH crap... That goes against the thread rule... Oh well. SCREW THE RULES.
I'll agree about the aliens, robots and UFO monsters in Earthbound, but I also hated fighting the trees that burst into flame when you defeated them, which would really knock down your characters' HP. I avoided every encounter I possibly could.
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