A horse walks into a bar
A horse walks into a bar. The bartender says, "Why the long face?" The horse says, "Because I'm an alcoholic and it's killing my family."
This is the deconstruction of another joke, where the horse says "I'm a horse". The original joke is fairly well known, so when the jokester substitutes this ending for the other one, it is unexpected. This is also sort of like black humor - it isn't really funny if someone's alcoholism is causing his or her family trouble, but under the circumstances it seems pretty funny.