To me, even the title is brilliant because it provides a fascinating example of what's called a copular verb.
In the show, the exact term "breaking bad" is never used, though Paul's character, Jesse Pinkman, once uses a conjugated variant to question why Cranston's Walter White has chosen to "break bad." Pinkman is a punk criminal who punctuates every other sentence with, "yo," so it's safe to term this as slang. From the context, it's clear he means "to turn to a life of crime" — similar to the way "go rogue" is used in spy thrillers. So this "break" can be understood as a rough equivalent of "become."
Urbandictionary.com says that "to break bad" can mean "to go wild, get crazy, let loose, to forget all your cares and just plain not give a sh**, to have a great time, to break out of your mold." It can also mean "to completely dominate or humiliate through sheer superiority" — a definition that's poetically apropos to some themes in the show.
Notice that this "break" is different from the one in "to break bread," "to break news" or "to break a leg." In these, you're breaking something. There's a thing being acted upon — a noun — that serves as the object of the verb. So the "break" in "break news" is transitive. In fact, that's the definition of a transitive verb: One that takes a direct object.
An intransitive verb does not take an object: to run, to speak, to drive, to recline — these are all intransitive because they're not done to something. They're just done. Many verbs can have both transitive and intransitive meanings. For example, if someone asks what you do on weekends, you might use the intransitve "I walk" or the transitive "I walk the dog."