First of all, overhauling your engine is ‘recommended’ not ‘required’ for part 91 operators as long as an A&P said you’re airworthy in the last 12 months. Manufacturers set forth a recommended Time Before Overhaul (TBO) for every engine. Continental and Lycoming engines are 12 years and their flight hours vary from 1,200 to 2500 hours.
Continental TBO can be found here. Note: the majority of engine models manufactured after February 2012 have increased TBO’s by 200-400 hours depending on flying frequency. The 400 hour TBO extension is only earned on some models by flying 40+ hours per month.
Lycoming TBO can be found here.
Lastly, if you want to see TBO by popular aircraft, click here. This is a good resource if you’re in the market to buy a plane and you want to find something with a high TBO.