I've heard success stories of people making millions from adsense or from creating software products. It's made me think who has been the most successful at building a company as a sole proprietor.
I guess we should discount companies that have single ownership but outsource all the work.
By my definition, for example, I run the most successful single-person business that I'm aware of. But it doesn't make millions, so it might not meet your definition at all.
My goal was to replace my day job with a software business that required as close to zero attention as possible, so that I could have time to spend on the things that actually matter to me.
The business brings in the equivalent of a nice Senior Developer salary, which is not what most people think of when they imagine a successful Startup. But it lets me work with a bunch of cool tech when I want to, and, more importantly, is automated to the point where Customer Service involves a quick 30 second - 10 minute email sweep over morning coffee. For me, that's a lot more valuable than a few more million dollars in the bank.
The cool thing about running your own business is that you get to decide on your own definition of success.
EDIT: I wrote a bit about how I got into this position, in case anybody is interested. It's not actually all that hard to do:
http://www.expatsoftware.com/Articles/guy-on-the-beach-with-...