I'm not sure on which area of programming you are focused, but until recently I was doing contract development exclusively and more often than not beat out people with Bachelor's and even Master's.
That being said, the reason I've been successful has nothing to do with intelligence or years of experience. I have gone out of my way to find contracts with Fortune 500 companies starting in 1994 with EDS followed by Blockbuster / Viacom, Sprint, Disney, Darden and other well known companies. I've actually taken less money to work for some of these companies because I know that people read our resumes very quickly and look for things that stand out.
Degrees over almost everything else are important if not critical if you are looking for temp to perm or contracts with companies that require it, obviously. However, you could hand two resumes to someone with absolutely no knowledge of programming and they will immediately recognize the names and form a strong opinion.
Another thing that I believe has brought me success is the fact that I decided in 2004/5 to focus exclusively on N-Tier, .Net, C# enterprise web applications. I've actually passed up contracts even though it might be another week or two so that I can maintain a resume that speaks clearly to a specific technology. The bad thing about web development is that it changes faster than Florida weather. The good thing is that if you keep up with the cutting edge technology such as Angular, SignalR, Breeze and anything else that is coming up you will never want for work.
While my post title, "No College for Me" may offend a lot of people, my belief is that you must do what you can to be marketable and stand out. If I stand side by side with someone with exactly the same experience and focus, they will get the job if they have a degree. On the other hand, I landed the contract at Blockbuster / Viacom in December of 1996 because I had just received a Microsoft Certified Professional certification in Windows 95 so had a large logo at the top of my resume. I am currently working on my (they keep changing it) Microsoft Certified something relating to developing applications. When I put that at the top of my resume I believe that it will again trump most if not all degrees.
On a related note, I went to Orlando Code Camp this weekend. There were 789 males and one scarily hot Goth girl with a mini skirt and some disturbing yet erotic tattoos. Damn, I'd like to see her code.