In Ireland, 1959, the Monaghan's baby daughter Alice has been stolen and replaced by one of the faerie, so Hellboy is called in to investigate. He outs the faerie, a changeling named Gruagach easily enough, but getting Alice back from the faerie will come at a price. He has until sunrise to bury the corpse of Tam O'Clannie, a rogue the faerie king Dagda was rather fond of, in a grave in one of three churches. And thus begins a rather macabre buddy-comedy road trip, especially since Tam's still pretty talkative for a dead guy.
Although Mignola didn't care for The Corpse after he first published it, it's now one of his favorites, and many fans feel the same way - myself included. There's even a reference to The Corpse in the first Hellboy movie, which has a scene of Hellboy depending on a curmudgeony corpse as a guide. I think part of the appeal of this one is that it's a lot of fun, lighter than most other Hellboy comics I've read, despite the bittersweet ending. Part of this stems from how Tam plays off Hellboy, from Tam wanting to take a detour to dig up some buried gold (leading Hellboy to wonder what he could possibly use it for, since...y'know...he's dead) to Hellboy having to retrieve the corpse's arm after the fight with Grom. On a darker note, the events of this story would have huge ramifications later on down the line, particularly in the final three Hellboy story arcs.