Does coffee really stunt your growth? I have heard that coffee (or other chemicals such as caffeine in it) can actually prevent you from growing. Is this really true?
No. That coffee (or caffeine or anything else in coffee) would stunt growth is a debunked myth.

Here's an article from the New York Times that cites a small university study that showed no relation in bone density/gain in adolescents. Another article from Smithsonian cites the same article and a few other studies from the NIH and others that show very little impact of caffeine / coffee on related growth factors, the other factors which are largely explained by other factors (e.g., sugar or other stuff from other types of beverages).

That said, caffeine and other chemicals in coffee have certain other effects, and certain people are sensitive. Here's a related article about some other coffee myths.