This is an idea I've been kicking around for a while. Hellboy is by no means Jesus. In fact, he is possibly as antithetical to Jesus as one can get. I mean, for all intents and purposes he is the beast of the apocalypse. He is prophesied to end the world at the head of a demon army. HE HAS A CROWN OF FIRE. THAT IS PRETTY ANTI-CHRIST RIGHT THERE.
And yet, Hellboy is a self-sacrificing hero. He constantly stands up for his friends. He is, as Tolkien would say a "Eucatastrope". Note the roots of the word- Eucharist and Catastrophe. He is constantly getting his big red ass handed to him in the name of saving the world. It's rather heroic for a guy with horns and a tail.
Let's also look at Hellboy's origins for a second. He has a divine (ok, demonic, but whatever) father and a Human mother. Furthermore, just as Jesus was the descendant of King David, Hellboy is the descendant of King Arthur. He is often tempted by Devils and the like to give into the temptation of his nature but says no, often with punching. I'm pretty sure that happened to Jesus too when he was in the desert (punching depends on which translation of the bible you have).
Another key aspect of the entire christian mythos is that whole resurrection thing. In Strange Places, Hellboy actually spends some time dead and comes back. In fact, he's been mortally wounded many, many times. Hellboy is deathless. He is incredibly hard to kill, and even if you manage to get him he comes back. And to add more to the parallel, after he leaves the BPRD he spends time wandering around helping people. His gun is called "the Samaritan" for a reason.
And, one final point, is that one of the ways Big Red can save the world is by simply ceasing to exist. Getting rid of his right hand of doom solves a lot of problems, but he wouldn't be there to save people. It's a big dilemma, to be sure. It's his cross to bear, if you will.
So Hellboy is Christ figure to be certain. But if we accept that there is a whole new question. Can a demon be a good dude? Well, this brings into question ideas of Nature vs. Nurture. Hellboy was raised by Trevor Bruttenholm, who is always shown as a good father figure. Despite his demonic origin, Hellboy has been raised by humans much like Jesus was. If Jesus had been raised by someone evil, how might he have turned out? Jesus may be the son of God, but he's often referred to as the "Son of Man". Hellboy and Jesus may both have had parents who were divine, but the ones who were their human parents. Mary and Joseph and Trevor were the ones who took the time to raise their kids right. Otherwise, who knows?
It's easy to turn the Big Red Ape down for Christ figure status. After all, he is a horned, hoofed demon with a tail and a gigantic stone fist. No one would blame you for saying that he is more of an anti-Christ figure given that whole Anung-Un-Rama great destroyer thing, but at the same time he's done a lot of good works in distinct contrast to and as an attempt to escape his destiny. I for one give the guy some credit. He's a good bro at the end of the day, and his human upbringing and resistance to temptation shows his true character better than a pair of horns.