No, you are not required to accept an offer that meets or is above your listing price. A listing price is a benchmark as to what a seller is considering selling their home for. It is not an offer. An offer, if accepted by either buyer or seller places you in contract. Because the listing price is not an offer, this rule does not apply.

Fore example, if you had you home listed for 200,000, and someone offered you 225,000, you then suggested 300,000, and they said yes... your suggestion of 300,000 is a counter-offer to their offer. If they accepted 300,000, you would then be in contract. Understanding this difference is important. Your real estate agent should inform you of this difference, and represent your final authority as to accepting offers presented to you.