How do you know what you're worth?Think about what you need to make, and double it. Then double it again. You're probably getting close to what you ought to charge. I expect to pay $50-$200/hour when I hire a contractor (depending on whether they are famous for what they do or not), and when I did contract work I billed at $125/hour. I was reasonably well-known for the field I contracted in, with a published book and code sprinkled throughout the project I supported, and my name appearing daily on the related mailing list--I probably should have been charging more, as I never lost a customer because I cost too much.
Someone once told me that if you, as a contractor, don't get a response of "fuck you!" in response to your estimates about half the time, you aren't charging enough. That's probably really good advice. You'll work less, but work better, because you can really devote yourself to the clients you do have. This assumes that you are really good. If you aren't really good, then you'll just have to take what work you can get at whatever rate you can get. Doing fantastic work fast is more important than working cheap, because people will recommend you if you're good and expensive (they'll say, "This guy is a bit pricey, but he does amazing work") but probably not if you do crap work and don't pay enough attention to them (if they say anything at all about you, they'll say, "I can never get this guy on the phone, and he does sloppy work, but he works cheap").
If you were hiring a contractor, which of those choices would you call? And which kind of customer would you rather work for? The cheap customer always demands even more than he's already getting, and expects to be treated like a king for it. The customer that wants great work is grateful when he finally finds someone that will deliver--at just about any price.
Also note that the larger the corporation, the more you need to charge to deal with their red tape. You will have to invoice according to their rules, you will have to keep yourself updated in their vendor database, you will have to deal with additional tax forms, and you will have to get sign-off on projects from more people. Working in a big corporation will also drain the life from you at an alarming clip, because they will have meetings over the stupidest crap--you'll be getting paid huge sums for eating donuts and listening to endless arguments over what to name a table or a variable, but you will probably die a little inside, as well. After my first couple of experiences with big corporations, I began to charge extra for soul death (that's not how it appeared on the invoice...I just added another $25/hour to the rate).