I did exactly what you are contemplating; I was 14 though, and it was high school that I dropped out of. I spent 4 years at home studying C, OpenGL, Calculus, and Physics. I worked on lost of little personal software projects, most of which were physics simulations utilizing OpenGL for rendering, or sometimes just ncurses. I also occasionally took low paying internship-like jobs whenever I could find them. Note that these weren't full-time, and they only lasted for a few weeks or a few months. They involved helping out at small tech support departments at various institutions.
When I was 18 I put together a resume listing my internships. I also collected videos of my physics simulations into a portfolio which I posted online. I took all this to a company in New York and got a full-time job as a Perl programmer. It paid pretty darn well for my age. I had health insurance there, a retirement plan, and all of that standard "real job" sort of stuff. The company was medium sized, about 25-30 people.
I've been making progressively more money ever since. I'm now 22 and I've been living comfortably on my own. So yes, it's definitely possible. I imagine that doing that sort of thing is possible in just about any field provided that you have enough wits and motivation, though software programming is probably a particularly easy one.
As a postscript to this story, and as a warning to you, I will mention that lately things have been going totally awful for me software wise. I was 14 when I started, and I'm 22 now, so it's been 8 years. Over those 8 years I spent close to 12-hours per day in either Emacs or an xterm, and the non-stop typing totally destroyed the tendons in my hands and arms. The horrible ergonomics at my desk probably didn't help either. Currently I can't spend more than 1-2 hours at the computer without getting horrible pain in my hands, and twitching in my fingers. I've had to stop working, and I'm moving back home with my folks until my hands heal, and until I can find a different career (hopefully something utilizing my math and physics background, and with less typing).
So, if you're going to throw yourself heart and soul into the software world, then forget college, and just go for it. I think you'll succeed just fine, assuming you're smart and skilled enough. Though good luck finding a girlfriend in the working world, unless you already have a very active social life outside of school, or unless you already have one ;-)
Do research RSI and typing injuries tough. Maybe look up what happened to Richard Stallman's hands if you want to get some fear into you for motivation, and also James Gosling. And get a properly adjustable chair, and a good split keyboard:
(they also have an OS X model)
Best wishes :-)
If you would be curious to swap Skype or IM handles then send me a private message here on the forums, I'd be more than happy to talk.
Ouch, typing hurts. Back to the vector calculus textbook I go.