The pressurized water reactor has been the system of choice for the nuclear powered ships of the U.S. Navy, especially submarines. While not all
of them have carried this design, it has been the most standard propulsion
system in the fleet since the inception of nuclear power.
Such reactors have one natural advantage for use at sea - their primary coolant is available by the gigaton all around. While raw seawater certainly isn't the preferred option, this does mean that the reactor isn't carrying around important components that may be dangerous to mix with the surrounding environment. One example of the latter type is liquid sodium, a coolant used in some reactors; the advantage of the liquid sodium type reactor is that in the event of systems failure, the coolant itself has the heat transfer capacity to restrain the core, whereas water must be circulated to avoid overheating. The problem for naval use, of course, is that when sodium and water are mixed, well, bad things happen.
For submarines, the main disadvantage of the pressurized water design is that given above - they require water circulation at all times to avoid overheating. While the water itself may be plentiful, there are many times when a submarine would like to make as little noise as possible - and circulating water under pressure is very difficult to keep silent. At power levels above minimal, furthermore, maintaining this circulation will require the use of pumps, which have their own problems when it comes to quieting.
Having said all this, it is notable that the U.S. Navy has never (to my knowledge) suffered a reactor failure that has led to the loss of a ship. While most of the responsibility for this can be laid squarely on the personnel who man those reactors, and the culture of safety that trained them, it must be said that the pressurized water design does appear to have been the proper choice, despite whatever operational disadvantages it may have.
A minor quibble with the estimable smartalix
I don't count the U.S.S. Thresher because the initial casualty was a piping/valve defect (design or manufacture, I don't know for sure). The flooding in the reactor spaces was not, in fact, minor; the submarine (which typically maintains slightly postiive buoyancy) sank despite a surfacing blow and a partial 'emergency blow' of the reserve ballast tankage. Later, when the boat was being raised, it made it almost to the surface before it broke free and sank to the bottom rapidly. None of this would be consistent with anything less than a massive flooding of the reactor spaces. While the second surface attempt (the salvage) might have been due to slow, long-term flooding, if the boat was unable to initially blow enough to achieve positive static buoyancy, then the flooding must have been fairly rapid to offset the primary and reserve ballast systems in between the onset of the leak and the commander's order to emergency blow.
In any case, blowing the ballast (as well as the reserve) requires no electrical power (at least, not in emergency procedures) as it relies on stored compressed air, and the boat wasn't far down enough at the time of the incident for its air systems to have been overcome by outside pressure. The electrical shutdown did, however, mean that the plane controls probably failed, which would mean that the sub would have been unable to use forward motion to angle the boat upwards. This might have saved them, by giving them enough time (on battery propulsion, if available, or even on the boat's momentum) to offset the descent long enough to restore power, or at least reach surface and abandon ship.
So, the Thresher was lost not due to a reactor failure but due to a questionable design choice made in the boat's attitude and propulsion control systems. The reactor performed as expected, and when the short circuit occurred, it shut down (as designed) to prevent the loss of the control systems from causing an uncontrolled run (meltdown). As an indication of the success of this design choice, the reactor vessel from the Thresher (closely monitored by the U.S. Navy since the accident, as well as occasionally by civilian watchdog organizations of various nations) shows no sign of leaking radioactive material or radiation; the remains of the Thresher are radiologically nearly identical to the environment.
I'm not aware of any other U.S. submarines lost due to reactor system problems. The U.S.S. Scorpion was lost (it is presumed) to a hot-running torpedo, and those are the only nuclear U.S. boats to have gone down, unless I'm missing an experimental boat somewhere.
Whew. It's a good point to bring up, though.