The scene in the first movie right after Hellboy has killed a monster while holding a box full of kittens. The young lady who owns the kittens comes forward and without caring that this is a huge, red guy with horns, a tail and the word "hell" in his name, she smiles at Hellboy with genuine appreciation, and he pets one of the kittens with the finger of his huge hand.
Lets explain that: Perlman volunteered to do it even though they could have gotten somebody else. He sat through four hours of make-up. The article even suggests (though this is ambiguous) that he personally paid for lunch for everybody there.
No, he sat through four hours just to get the makeup on. It takes another four hours to get it off. He literally sat through eight hours (an entire third of the day!) of makeup work just to make this kid happy. Somebody give Ron Perlman a medal!
Manning and Hellboy share one after they neutralise Kroenen. Hellboy tries to light a cigar, but is out of lighter fluid. Manning at first sounding like his Jerkass self tells him he's lighting it wrong and gives him a wooden match saying it preserves the flavor. Hellboy tries it and to his surprise he likes it that way and they promptly thank each other for saving each other.
Bruttenholm and Myer's scenes together has a whole mentor student thing. And the reason Myers was chosen in the first place was so Hellboy would have someone to look after him as Bruttenholm did.
Abe and Nuala having a LoveAtFirstPsychicTouch moment, then later bonding over poetry and their shared psychic abilities. Also, the fact that he vouched for her when he didn't even know whose side she was really on. She tells him later how brave it was of him.
Hellboy going out of his way to rescue a box of kittens when Sammael attacked. Also, their owner fighting tooth and nail to save them before the monster could get to them.