Well, it looks like I can't resist the temptation to start a classic Sailnet flame war here. So grab some popcorn and sit back!
I have never taken someone else's private mooring ball, and have no immediate plans to do so, so this is somewhat academic. But I can imagine a non-emergency situation where I might be tempted, so it's worthy of some discussion.
First, I assume that all of you are referring to moorings that have been placed into public-access waters by private citizens. If so, my question then is, what gives someone the right to claim the water that immediately surrounds his Chlorox bottle, old LP tank, or Sur-Moor float? Suppose I pull into a small, protected cove with limited space, intending to anchor, but I find a bunch of moorings that people have left to "claim" their spot? In this hypothetical example I am envisioning a weekender's cove where the owners drop unregistered balls and use them maybe one day a week on average (not for daily mooring). There is no space left for me to anchor because the necessary rode would guarantee that my boat collides with or my rode gets fouled on all these mooring balls.
In this example, what is someone supposed to do? Do these people have a right to "lay claim" on public waters by littering the limited space with a bunch of unlicensed mooring balls? Do I risk fouling my anchor line on their balls by anchoring? Or, since the cove is littered by a bunch of unused balls, do I just grab one? Would it be any more satisfactory for me to just drop my anchor 10 feet away from his ball and claim "his space" without actually using his ball?
This is not a purely hypothetical example. The Delaware River has very few protected coves for anchoring, but there is one cove about an hour's sail away that I may want to try out in the next few weeks. Last time I was there two years ago it was filled with a bunch of unused, unregistered mooring balls (old LP tanks and the like), and although it was not so crowded as to prevent anchoring, it would not take many more to render anchoring unsafe. Right now I don't know what awaits me next time I go back there.
In general, I think some of this bluster over owners' rights to the mooring fails to recognize that the owners of unlicensed moorings are borrowing public waters, and should therefore expect that there may have to be some occasional sharing involved. At the very least, they should allow the "intruder" 10 minutes to leave without an angry scowl of indignation. If they don't want to be inconvenienced by this, perhaps they could post their expected return time on the ball with a request that the ball be vacated prior to this time.
Of course, if the owner is licensing his rights to the water from a regulating authority with a licensed mooring ball, then that's a different story. So my question to all of you much experienced cruisers: Are most of these mooring balls just dropped by owners who are "squatting" on the surrounding space, or are they usually leased from a regulating authority? I think that distinction makes a big difference.