For instance, two recent movies that I really wanted to like, Green Lantern and Captain America, suffer exactly the problem you describe. Cap's only 'problem' throughout the movie is 'will he get the girl?', or 'will he stop the Skull?'. Despite losing his best friend Bucky, we never get the feeling Cap paid a price, or that he had to overcome a personal price or shortcoming before the end of the movie...
So despite a healthy budget, capable direction and a recognizable protagonist, Captain America failed to reach beyond a mediocre premise and story execution.
I completely disagree about Captain America. For more information on my opinion, my posts are in the thread on that topic.
In a nutshell, Cap has to make a decision to give up the girl to save America. It was very moving.