Alternate Character Interpretation: While it's obvious Henry is enough of an irredeemable sociopath to kill for fun and turn on Becky when it suits him, there are points in the film where he shows emotion outside of a murder spree. He fondly recalls some parts of his childhood, and he seems to be enjoying himself when playing around with the camera he and Otis have stolen. Since he doesn't seem to be socially skilled enough to "fake" emotions, is he a true psychopath, or something slightly different?
The title character Henry is a man who finds feeling only in murder. Henry kills several people randomly and explains his strategy for getting away with it in that he always mixes up his MO. When Henry befriends a twisted man named Otis, the two murder a whole family, snapping the young son's neck on camera. He murders Otis after catching him raping his sister Becky, who confesses she loves Henry. The next day, Henry is seen leaving alone, dropping a heavy, bloodstained suitcase in a ditch that contains Becky's remains.
Hilarious in Hindsight: The movie is based on the confession of alleged serial killer Henry Lee Lucas. It's now pretty well established that Lucas, while probably a murderer, was also a massive bullshitter who made up most of his confessions.