We see some of this internal conflict in the first two Hellboy movies and based on Ron Perlman’s comments at Motor City Comic Con (via Dread Central) it appears that the third film would have dealt with the idea of Hellboy’s destiny as a destroyer and brought the plot line to a close.
Within the Hellboy universe, the character’s true name is Anung un Rama and he is the harbinger of the Apocalypse.
Considering that the character was raised catholic, he has a bit of a problem with the idea of bringing about the end of the world, leading to an internal conflict between his internal nature as a demon from another dimension, and being raised among humans.