Excellent question!! Unfortunately, a lot of sailboaters seem to think so.
It depends on where you are. Assuming you are not in the middle of the ocean (as in, more than 50 miles offshore) and you are in an area where things like supertankers and container ships are an issue, chances are very good that you are operating in an area which is designated as a narrow channel, fairway, or Traffic Separation Zone. You'll need to look at charts and Coast Pilots for your sailing area to determine where these are. In any of these areas, a sailing vessel, a vessel engaged in fishing or a vessel less than 20 meters in length (about 70', meaning basically any boat anyone is likely to own) is not to impede the passage of any power driven vessel greater than 20 meters proceeding withing the channel, fairway or TSZ. Similarly, such large vessels are generally expected to stay within the channel, fairway or TSZ in order to avoid smaller boats.
A very simple and elegant way to know if you're in or out of a TSZ is to set the buoys which mark the center of it as waypoints on your GPS chartplotter, create a "track" from waypoint to waypoint and set your crosstrack error (XTE) at whatever the distance is from the center of the TSZ to the outer edge of it. Then, as long as your XTE is greater than this, you're safely outside of the TSZ and presumably safely out of the way of the supertankers.
If you DO happen to be far offshore, then yes, your sailboat does in fact have right of way over most ships. But your best option is still to hail them on channel 16 and make passing arrangements.
Navrules, Rules 9 and 10