As long as you continue paying your utility bills on time, they have no bearing on your credit score. Although you cannot improve your credit score by paying utility bills regularly, they can still worsen your credit. Most utility companies do not report late payments the credit bureaus. However, if you refuse to pay after many notices have been sent, they may send your account to a collection agency. In such cases, a collection may appear on your credit report and this can be very bad for your credit score.
Note that the above applies only for the standard FICO credit scoring system. There may be other types of credit scoring models used by lenders and some insurers or service providers do consider your utility payment history, especially when you are signing up for gas, electric, mobile phone, cable, etc. If you do not have a well established credit history but have been paying your utilities on time for years, it will help.