Started my business back in 86 (1986, not 1886) as a part time affair and then went full time in 1987 and been running it ever since. It's computer software (an ERP class application for running administration in public schools). Other than just barely graduating high school, I have no degrees, certificates or such things.
I do have 21 years of making payroll every 2 weeks (never late), making lease payments and most importantly, making money. I've had as many as 30 folks working for me (now down to 10) and been through a disastrous failed merger (thanks dot-com boom!) as well as personnel issues, cash flow issues, stress induced sickness, etc, etc.
It's not for everyone and you're going to have times where you butt cheeks are clenching up to "code diamond" level. You have to be able to deal with stress (frequently and often sustained), be VERY, VERY familiar with your intended market (like work for someone in it for a few years first), be quick of mind and able to make decisions quickly (the trick is learning to make good ones). You ARE GOING TO MAKE BAD, AWFUL decisions -- just pick your self up, dust off, learn from them and go. Don't spend time wringing your hands over them. Now, if you aren't learning from them (i.e. you keep winding up doing the same thing), then you have a real problem.
Do not take debt on unless 1) you absolutely, positively have to and 2) you have a very good plan for how to pay it back while handling all your day to day expenses. I've never taken any debt on (grown through sales only) and I've watched folks go down more than a few times when they took on too much debt or took it on with only an ill-defined "hope" of how to pay it back.
Be very wary of "investors" -- if you ever go that route, be absolutely sure you can handle them trying to meddle in your junk. Regardless of "silent partner" type crap and not, the first time you have a financial hickup, they often start getting very loud and in your face. I've never taken on an investor -- but watched others do it. Only worked for 2 companies -- can think of at least 6 where they really really regretted it later.
Watch out for mergers -- they are seductive, but can really easily go south. I could write a small and boring book on this as I went that route and by the time it was over and extracted the remains of my company back, I had 1 employee for every 5 I had before that and tons of customer ass kissing to do for years.
Business plans -- I've heard from everyone they are the way to go and I can see it. My best two friends run their own IT company and are very plan oriented and for them, it's working out great. I didn't go that route (the plan was "obvious" to me, but I had been in the industry for a while and had thought it out before I started). If you do get one, do NOT be afraid to revise it as things grow -- especially early on.
All that said, I honestly could not even consider working for someone else. If you have the right temperament, aren't afraid of working your ass off for a long time (hopefully, not forever, but at least for the first 5 years), can intelligently handle risk and have done the basic research to insure your prospective business really can be viable, it really has many rewards (money, personal satisfaction, eventually ability to retire early, etc).
That said, there is a certain paranoia that always lurks in the back of my mind about what I'd do if this fails. Having no degree could mean a nasty dose of reality in that case. I'm not the only one -- about half of my close circle of friends run their own business and they are all successful to various degrees and most have been at it for 5+ years. To a one, they all have this sort of "what will I do if it fails" background dialog going something. I think it's a good thing :-)
In summary though, I wouldn't trade away a minute of it. Best thing I've done with my life (so far)