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!
Ryan Himmel, CPA and registered securities analyst, is the founder and CEO of BIDaWIZ.com, a professional network for small businesses and entrepreneurs to obtain trusted advice and services from a team of CPAs, Enrolled Agents, Financial Planners & Tax Attorneys. His team provides answers to the many finance and tax questions that small businesses encounter every day. Ryan has been quoted in The Wall Street Journal, Forbes, Fox Business and Crain's New York, among other publications. Ryan also regularly contributes to the community with his finance and tax blog.