One of the obstacles you'll have to deal with on the Sound and elsewhere along the Northeast coast is lobster trap buoys, commonly called lobster pots.
The ones you can't see because the current has driven them below the surface are the problem. Whether under power or sail, if you run one of these down, they tend to head straight for your prop. You'll know you've hooked one when you're under power because your transmission will emit an ugly whack. Throtttle back and get it out of gear immediately. Under sail, you'll just come to a slow stop.
How you deal with being anchored by your underwater appendages depends on a number of factors.
If under sail, the line doesn't always get wound around your prop and shaft, so you can generally get free by backing your sails. If under power, you probably have the line and possibly even the float wrapped in your prop.
There are all kinds of ways to get out of this situation, but the desired result is to get clear while leaving the lobster fisherman with a way to retrieve his valuable trap.
If you simply cut the line below your prop, you can still wind up with a tangle in the prop that has to be cleared and will leave any critters in the trap to die of starvation. In this case, the first order of business is to get the strain of the "anchor" line off your drive train. Use your boat hook to get hold of its descending part and work it forward to the bow and cleat it off, but leave a lot of slack on the part that's wrapped in the prop. This will swing the boat upcurrent. Now, sit there until the current goes slack. Going under the boat while anchored in a current will exhaust you in no time. Wave to any concerned passers-by, pretending you meant to do this and assure them you're OK. Once the current slows down, assess the wrap on the prop. Worst case, the line is so badly snarled you'll have to cut it. The object now is to do so while saving the trap, so cut the line going back to your prop at the bow cleat, leaving enough to attach a temporary float, such as one of the empty anti-freeze bottles you keep aboard for oil changes (you do have these, don't you?) Next, go overboard to cut away the tangle. If it's at all bouncy, use one hand to keep well below the bottom of the boat and watch your head. Make a number of short dives, or share the task with your crew for a great bonding experience ("Hey, remember the day we caught the lobster pot?") Check for any apparent damage to the strut, shaft, and prop by seeing if the prop spins freely. Once everything's clear, tie the original float to your temporary float. This will tell the lobsterman why he's short some line, and maybe he'll take the hint that he needs a longer one and a bigger float.