This one might more appropriately be filed under "Unexpected comic strips," as it's a bit of a strange one. While nothing that David Lynch does is necessarily expected, a newspaper comic strip is not the first thing one would imagine a surrealist film and television director might do. Even then, if one tried to imagine of what kind of comic strip said surrealist film and television director might create, I don't think it's likely anything like The Angriest Dog in the World would come to mind.
David Lynch is best known for his movies such as "Eraserhead," "The Elephant Man," "Dune," "Blue Velvet," "Mulholland Drive," and others, as well as his television series "Twin Peaks." Before venturing into film, he originally wanted to be a painter. As such, his films were supposed to be paintings come to life, if such a thing is possible.
In 1983, he decided, for reasons known only to Lynch, to create a comic strip that featured a dog who, according to the caption which accompanied every strip, "...is so angry he cannot move. He cannot eat. He cannot sleep. He can just barely growl. Bound so tightly with tension and anger, he approaches the state of rigor mortis." Each strip then featured four panels, three of which were identical and showed the dog outside being silently angry during the daytime, and the last which was a similar scene showing the dog outside at night. The images were exactly the same in each strip, the only difference being the speech balloons which emanated from inside the house. The dialogue ranged from philosophical observations to bad puns to generally meaningless statements, though I think Lynch believed the idea of the strip was far more interesting than anything that was said in it. The dialogue of those in the house didn't matter as much as the fact that a terminally angry dog was sitting out in their yard being entirely ignored by them.
According to Lynch, the idea came from a time in his life years earlier when he was attempting to work through a large amount of anger. He says that he had originally decided to see a therapist, but that the therapist informed him that therapy would seriously impede his creative process, so he decided against it. He instead discovered and began to rely on transcendental meditation, which he says helped him overcome that anger and allowed him to create his body of work. The strip, then, is a look back at that angry period of his life and the outlook on the world that he had during that time. In a way, it seems that it's supposed to be comedic, but as Lynch put it, "...the humor in the strip is based on the sickness of people's pitiful state of unhappiness and misery." Whether one finds that funny or not is up to personal taste.
The strip only ran in alternative weekly newspapers, most notably the L.A. Reader, for nearly 10 years. This is remarkable, especially given the negative response that most readers had to it. When it began to be published in the Dark Horse anthology Cheval Noir, a letter from an angry reader called it a "useless, idiotic, CON GAME of a strip." Far better strips have run for far less time, though it's possible that someone as popular as David Lynch can get anything published for however long he wants.
For more information:
The Angriest Dog in the World at Toonopedia
David Lynch at Comiclopedia
A selection of strips at The Universe of David Lynch
A further selection at LynchNet
David Lynch at Artsy, which showcases his artwork outside of film