For what reasons can you be put under military arrest?

First of all, in order to be placed under military arrest, you must first be a member of the military. Federal law provides protection to private citizens against being policed by the military. In fact, Martial Law must be declared in order for the United States Military branches to have "policing" powers over the general public.

As far as a member of the military being arrested, they can be arrested by civilian or military law enforcement for a multitude of offenses. Anything from disorderly conduct, public intoxication, to murder can get you arrested as a member of the military. As a member of the military, whatever charges you face placed upon you by civilian law enforcement, you can face the same charges from the military. Double Jeopardy does not cover you in this regard.