I realize that the question depends a lot on the actual project and the qualifications of the applicant, but I would really appreciate some examples to get an idea.
Assuming your business has only one person to pay (you) then it's likely that expense is going to be the largest of the company. How much you should be paid is a personal question. How much do you require for your lifestyle? How much would you be able to make if you were to simply leave your business and work for someone else (this assumes that this is a readily available option.) You don't want to be taking a salary cut while slaving away on your business. Additional considerations are things like adjusting for vacation pay, sick days, insurance and all those other things an employer might pay for. Once you have decided how much to pay yourself, you then need to add business expenses such as accounting services, rent for an office (if needed,) cost of business tools, etc.
At this point you have an idea of how much your business is going to cost to operate (which includes paying you.) Now you simply figure out how many billable hours you can get within x period and do the math. However, you need to keep in mind that if you decide you will work an 8 hour day, not all of those hours will be billable. You will also likely have downtime between projects.
Again, do the math. Now you have a basic idea of what you should be charging per hour to make your business work and to provide reasonable pay to you. One great way to break outside the hourly rate straight jacket is to give a fixed cost. Sometimes you can "crush it" on a fixed project and bring in the equivalent of a much higher hourly rate.
Last step, go sell! If you get this last step right, then your hourly rate may be meaningless. Double your rate and still get the clients rolling in then you are a natural!