While it's true that you probably won't be asked about a degree in the professional art world, I wouldn't let that dissuade you from attending an art school to learn the discipline. I'm studying illustration and design and I feel like the type of education I'm getting is great, and that I wouldn't be able to learn the sorts of things I'm learning anywhere else.
Amount of times I've been asked about a degree while negotiating a freelance job: 0
If it's a good program, and you can afford it, then it won't hurt, but if you aren't self motivated enough to theoretically do it without, the school isn't going to imbue that into you. Most professionals (like the really big timers) I know don't have accredited degrees in art. Lots went to the Safehouse Atelier, a select few went to AI and its ilk, and the rest are 100% self taught. Don't waste 4 years in a crummy program for a degree, because the actual learnin' and the people you meet are all that matters, not the paper.
(This is all from my experience in freelance illustration, by the by. Graphic design/advertising art are possibly different.)
Getting a degree in any sort of art is one of those things that may or may not actually matter. When it comes down to getting a job, it doesn't matter at all, all you have to do is show you can do the work. They don't look for a degree, they don't care, you can graduate and still be a horrible artist. It won't increase your liklyhood of getting a job.
Yes, on the one hand you do learn things you might not otherwise, but you also go into debt that you probably won't be able to pay off.
I'd say 99% of the professional artists I know (and I know a LOT), ones who make 100% of their income off of art, haven't gone to school for art. Many of them do have a degree, but it's not related to art.
Ideally, a BFA should gear you toward a job as a gallery artist, graphic designer or illustrator. If it doesn't do that, it isn't a very good program.
But even if it's a good program, it does tend to come down to how much effort you put in it. And you could put that same effort into teaching yourself, but--a BFA program will expose you to things that you didn't think to look up on your own, and it will end up influencing your taste because you'll be required to study things like art history... and there will be that teacher every now and then that tries to bend you into a particular shape and if you value your grade, you'll do it. Sometimes a good thing, sometimes a not so good thing.
Some time you will probably have to read boring articles about the importance of tree stumps in 19th c. American landscape painting, but I'm sure every major has its amazingly dull moments.
You can go and get your masters so that you may qualify for a teaching position, yaay! Otherwise, a degree in fine art doesn't do anything for you. A good portfolio, a strong skillset, and good PR will get you work. Bachelors of Fine Arts are a dime a dozen.
Save your money and teach yourself. A degree in art is not going to get you far in life. If you're good then your art will sell. A piece of paper and a bunch of pretentious art teachers is not the way to go in becoming a better artist.