As with all animals, growth ceases once the growth plates on the bones have fused, which happens at approximately age 21 for the average human female. Men generally reach their maximum height by the age of 25.
Every person is different, so some people may continue growing for several years even after having passed up this approximate stopping point. There are also some disorders which cause the body to not produce the chemical signal which stops bones from growing longer. As of 2014, the tallest woman alive is a Chinese woman in her 40s named Yao Defen; she is seven feet eight inches tall.