How old do you have to be to rent a car in Utah?

This is more dependent on the car rental company than the state. As long as you have a valid, unrestricted drivers license, you can drive any car. However, most car rental companies do not let anyone under the age of 25 rent a car.
If you are between 18-25, you might be in luck with a smaller car rental company, but don't be surprised if you get charged some type of extra fee.