My best friend is a Major in the Georgia National Guard. They participate in all kinds of events without Gubernatorial requests.
For civilian events in other states? To avoid posse comitatus restrictions they have to be requested by the governor of the state they go to. And news reports said that the MA government requested the NY National Guardsmen (anti-terrorism unit) to be deployed to Boston for the marathon. Each state has their own anti-terrorism unit but NY and Florida (?) have an extra unit as well.