In CoD:BO, in the radar tower mission where the guy (who was, until now, faceless and storyless) falls off the gantry when the RPGs hit it, I was compelled to replay the part until I shot both RPG guys. Long story short, 20 restarts later, I hit both with more than enough bullets and the second one wouldn't go down, he was invincible until after the RPG was loosed.
In God of War 3, the way they characertised Pandora just suckered me in, making him the polar posite of Kratos. Just sat there after 'that' cutscene in disbelief...
Finally, from when I was about 6, Croc: Legend of the Gobbos had your typical "Continue or Exit" screen when you lost all of your lives. I got fed up with dying and hit exit once and Croc just shuffled himself offscreen slowly, head hung low . Made little me cry, I thought I'd broken his little heart.