What is the average length of time for a utility patent to be approved?
The USPTO says in its FAQ from 2003 (http://www.uspto.gov/main/faq/)
-- Currently, the average patent application pendency is 24.6 months. Applications received in the U.S. Patent and Trademark Office are numbered in sequential order and the applicant will be informed within eight weeks of the application number and official filing date if filed in paper. If filed electronically, the application number is available within minutes. --
So just over two years - that said, I am willing to bet the variance is much higher since some patents can be quickly approved while others might need several back-and-forths with USPTO before they are. We had a few pending in our org in software and they were all 4-5 years old and still being discussed.
I am pasting a chart from a posting on the PatentlyO blog from this year showing the rise and fall of the average pendency. There is also data available by Technology Center. Pendency is from filing to either abandonment or issue. The time to allowance would be less.