In 2009 the United States graduated 89,140 students in the visual and performing arts, more than in computer science, math, and chemical engineering combined and more than double the number of visual-and-performing-arts graduates in 1985.
I come from an artistic family: both my parents were musicians, as are my wife and stepmother; our eldest is a fashion designer; our youngest is a songwriter; and I write poetry. Among the seven of us, we have lots of non-technical degrees (though I do like to point out that I was the only English major in my class on partial differential equations). And, of course, we have met many, many others who also have arts degrees.
With few exceptions, arts degrees are unlikely to be worthwhile. Art is, fundamentally, something an artist does, not something an artist studies.
The model for learning the arts is not the college classroom, but the master-apprentice relationship. Though I do think that anyone who wants to be a serious musician should spend some time in a conservatory learning ear training and counterpoint and harmony and such. Even so, the mentoring relationship is much more important: think of Nadia Boulanger.
The rest of the academy should be approached carefully. In the field I know best, a strong case can be made that the academicalization of poetry has utterly destroyed its audience: it is scarcely an exaggeration to say that more people write it than read it. The reason for that is simple: a comparison of "unknown verse not worth knowing" from the 19th century with similar verse produced today is instructive: the older stuff is usually technically competent -- on the level of a mediocre TV show, pleasant enough, but insignificant. The modern stuff is acutely painful to read or listen to (and still insignificant).
But what other visual and performing artists need is mentoring and work experience. A sculptor needs to learn to cast bronze. A fashion designer needs to know how to spec a design for large-scale production. A painter needs to learn to mix paints. A poet needs to learn prosody (well, OK: that's controversial -- the number of poets today who can tell an anapest from a dactyl is vanishingly small). An actor needs to act; a dancer, to dance. And for his acting, an actor will learn everything -- and dancers, well ....
On the performing side, I think we suffer from the self-esteem movement. My wife teaches voice and piano. It is absolutely the case -- as has always been true -- that no more than a handful of her students will ever make a living at music and extremely unlikely that any of them will make a good living at it. And yet they are all and always told how wonderful they are.
The mother of one of her students reported on a college fair at a local high school, where the most popular major investigated by the students was Musical Theatre. This major did not exist even 20 years ago. And a bigger waste of time and money can scarcely be imagined: one can have private voice lessons, acting classes, and dance classes for a fraction of the cost of college (and pay for it with the proceeds of food-service work!) and have the freedom to audition for professional jobs. If, after a year or two, one has not been hired, then one can simply move on to something else.
So -- if you want to be an artist, stay out of college. Find a mentor. Make art. Perform. Then, when you've failed -- and almost all of you will -- you can go to college (or not) with some idea of what you can and can't do. And you will not be carrying tens or hundreds of thousands of dollars of debt.