The first career option with an arts degree is that it leads very easily into a career in academia, that is as a university lecturer or professor. You would need to complete an honours degree, then a masters or a PhD.
Secondly, arts degrees have many majors, it depends on what you choose to major in. For example, if you majored in psychology, obviously you could go on to be a psychologist.
If you major in archaeology, you could go on to be an archaeologist who works at a museum, heritage institution, or at a university.
You could major in anthropology and go on to be an anthropologist.
Linguistics - linguist.
Cinema studies - film critic/commentator, a writer in newspapers, magazines, or on TV, or work in government departments like the Australian Film Commission etc.
The reason why people say an arts degree is crap is because, other than an obvious example like psychology, most majors in an arts degree don't lead to a specific qualification, unlike a degree like engineering (which obviously leads to a career as an engineer), or law (which leads to a career as a lawyer), or commerce (which leads to a variety of professional careers as an accountant, economist etc). The arts degree teaches you the skills and critical thinking required in your chosen major, the rest is up to you to develop your career path.