The Market Value of a Degree
Whether the market values your degree is almost entirely dependant on the type of profession you are entering and the type of degree you have acquired. A doctor must legally have a medical degree. Likewise a law degree is necessary to practice in most states. These are pretty significant gate checks if you are entering into these fields. So if you put in the time and effort to get an MD or JD there is a good chance the market will inherently value your education. Other notable additions are fields such as engineering.
What about those who have degrees in art, or business? Are those worth anything to a free market? The short answer is no, they are not. Whether you have a degree in music (like myself), English, or business, out in the real world you are judged on the quality of your output, not your education. Nobody ever hired me for a gig based on my college education, but rather for my demonstrable skill set and experience. Nobody will give you an advance on a novel because of your English degree, and nobody will hand you a $100k per year job because you showed up to business school for 4 years. The reality that the world will only reward you for your actual ability to produce is not something most people want to accept.
The Value of a Degree to You
Just because the world doesn't place any value on your degree doesn't mean it was a waste of time. A degree is a certification of knowledge, and knowledge is useful. Each class taught you a set of skills and imparted pieces of wisdom that may help you on your way, if not be directly applied to your goals as an artist or businessman. Of course, such things only have value if you choose to use them.
I've noticed that the people who value their own education the most are those who have the least to show for it in the real world. People who have achieved something of value, either to others (as in business) or for themselves rarely seem to talk about their education, preferring to let their work speak for itself. Those who have achieved nothing often feel the need to make their education their achievement, placing it outside of its true purpose and making it a thing unto itself.
I know I am more proud of my body of work. My songs, poems, screenplays and stories speak for themselves.
Learn by Doing
One final thing teachers never seem to communicate is that you will learn far more while engaged in your field than you ever will in a classroom. Great performers are taught as much on the stage as in the practice room. Great writers learn to craft incredible narratives by writing, not by analyzing Jane Austen. Successful business owners grow to understand their market and customers by serving them in the real world, not by taking statistics classes. Spend some time with a seasoned businessman and he will tell you that in the job market, experience trumps education every time.