The only way to be absolutely certain is to get X-rays of your long bones. With that said, if you are a female who is older than age 18 or a male who is older than age 21 then it is safe to assume that your growth plates have fused. The actual age at which the growth plates are completely fused and at which you stop growing taller varies a lot from person-to-person, but those general cutoffs are pretty safe, upper limit assumptions for most people.
Dr. Leonardo Noto Physician, Author, and Owner of "The Health and Medical Blog with a Personality," www.leonardonoto.com.
Disclaimer: Always discuss all health concerns with your personal physician (I don't count!) before making any medical decisions. The internet and self-education are great, but they don't replace your doc!