What document must be on board and available for inspection by enforcement officers whenever a vessel is operated?

Depending on your state or who's jurisdiction you are in will dictate what you need. In the US, most everywhere you go maritime Law Enforcement Officer's (LEO's) are going to want to see your vessels registration (if required). This will have the current owner, operators name, address, date of registration, hull identification number (HIN), weight, and length over all (LOA). Additionally they will most likely ask for a State ID. It is almost guaranteed state or local or Federal officers are going to ask for all the similar paper work. Including any special endorsements and licenses.