If it is a mortgage, I would say there's no need to pay off the debt as long as you believe you will be able to make your monthly mortgage payments based on your income or expected income.
If it is credit card debt or personal loans, I would say it is best to pay them off before you go into business - it would look better on your credit report if you are a sole proprietor and in case you need to apply for a business loan.
If you don't need a business loan or definitely think you can make strong, consistent income in the business, some debt would be acceptable as long as you stay committed to paying (securing a low finance rate wouldn't hurt either).
For more information on small business loans, visit the Small Business Administration at http://www.sba.gov/. There's a great assessment tool there that will help you gauge whether or not you're ready to start a new business (http://www.sba.gov/assessmenttool/index.html. Good luck to you in your new endeavor!