Since I've recently been doing a runthrough of the Mega Man series anyways...
Mega Man
Bomb Man's Sniper Joe getting stuck through a wall.
Mega Man 2
Heat Man's boss room. Right after the boss showed up, I accidentally opened the gate whence I came from and was warped to a ****ed up version of Wily's first stage. With boss music still playing. Graphics and palette were glitched, but I think the enemies were still intact. Stage was a dead end right before the Mecha Dragon segment.
Wood Man's stage. I mean seriously, not only am I being attacked by adorable robotic creatures, but a kangaroo-sized rabbit is firing homing carrots at me.
Mega Man 4
Being attacked by a giant hippo.
Finding out that if you shoot a boss while he's flashing, it not only won't hurt him but it'll make him flash even longer. Paired with the fact that touching a boss takes away a fourth of your life, this really pissed me off.