Testosterone is what makes you stop growing as it closes your "growing plates" in your joints. That is the reason men are generally taller than women (as girls go through puberty earlier so the estrogen causes their plates to fuse earlier and hence be shorter. Guys are generally taller because they start puberty later and have more time to grow when they are younger, so when the start puberty they grow from a taller height). Generally men stop growing in height at age of 25.
Generally, men stop growing in height at around 25 years old. Testosterone is what makes a man stop growing as it closes the "growing plates" in the joints. Men make the most testosterone during puberty, so once puberty ends, males tend to stop growing.