Is military service mandatory in America?

Americans have to register for Selective Service, but there is no mandatory obligation to serve in the Armed Forces.

Technically, Selective Service is a requirement to serve in the military, but one which it is the MILITARY's option to excercise. That is, if the military decides to draft people (which, is what the Selective Service Act codifies), then you MUST serve. There are conditions which the military may grant you either a temporary or permanent waiver from your obligation, but once again, the conditions for such a waiver are set forth in the SSA's text, and are not subject to the individual's decision.

That is, the US currently has a compulsory military service law, for men only, but choses not to currently avail itself of drafting anyone. To be clear, ANY man 18 to 25 currently residing - whether legal or not, and regardless of citizenship - in the United States for a period of one year or more MUST LEGALLY REGISTER for Selective Service. However, the U.S. Military is not currently conducting a draft, so registering does not mean you will automatically be called into service.