No, accident forgiveness does not cover speeding tickets in most cases. Nationwide and Travelers are the only major insurance companies offering accident forgiveness that covers minor moving violations like speeding tickets.
In some states, Nationwide's accident forgiveness add-on covers 1-2 speeding tickets every three years, while you need to buy minor moving violation forgiveness separately in other states. Accident forgiveness from Travelers is part of the company's Responsible Driver Plan, which covers one speeding ticket or other small infraction every three years.
In general, accident forgiveness is an optional policy add-on or a reward for customer loyalty that prevents the policyholder's insurance premium from increasing after a crash. Details vary by state and company, though. To learn more, check out WalletHub's complete guide to accident forgiveness.