Almost all male U.S. citizens and male immigrants, who are 18 through 25, are required to register with Selective Service.
It's important to know that even though he is registered, a man will not automatically be inducted into the military. In a crisis requiring a draft, men would be called in a sequence determined by random lottery number and year of birth. Then, they would be examined for mental, physical, and moral fitness by the military before being deferred or exempted from military service or inducted into the Armed Forces.
A CHART of who must register is also available in PDF.