Fuzzing as a concept is heavily underused in routine testing. People will usually focus on positive flows and some obvious/typical negative ones. But it's almost impossible to have the time to write exhaustive testing to cover all negative and boundary scenarios. But the good news is, you don't actually have to. There are so many tools now that can almost exhaustively generate tests for you at all levels. The bad news, they are not so widely used.
What do you use?