What is a safe passing distance for vessels?

According to Rule 16 there is no specified distance one must keep when crossing, meeting, or overtaking another vessel, other than, as the give-way vessel, you are to keep well clear

As to what distance a vessel may be required to take action to avoid collision, it will vary, however it should be in accordance with Rule 6, Safe Speed, and Rule 8, Action to Avoid Collision. These rules which state amongst other things that: Any alteration of course or speed shall be large enough to be readily apparent to another vessel and taken early enough to allow sufficient sea room for the safe passage of the other vessel and at a safe speed so that she can take proper and effective action to avoid collision and be stopped within a distance appropriate to the prevailing circumstances and conditions. 

The provisions prescribed in action by the Give-Way Vessel and Stand-On Vessel apply only when vessels are in sight of each other.