Back during WWII, it seems it was fairly rigid. 

Battleships - Named after states  (Arizona, Wisconsin, Missouri, etc.)

Cruisers or other capital ships - Named after cities

Submarines - Named after fish

Aircraft Carriers - Named after battles (Yorktown, Saratoga, Lexington, etc.) 

So how do they name them now?  There doesn't seem to be any kind of rule.  Submarines are often named after states or cities now, aircraft carriers can be named after famous people (including sometimes people who are still alive, which I don't think is a good idea), and then you have things like the aircraft carrier called the USS United States, which seems a bit redundant, as well as unimaginative. 

The small assault carriers used by the Marines seem to be the only ones still adhering to any rules - they seem to all be named after battles the USMC was heavily involved in:  Bellau Wood, Iwo Jima, Inchon, etc. 

Are there any rules?  Or is it just driven by whatever politician they want to flatter at any given time? 

"The degenerative and loony should never be denigrated but, rather, thanked. In their absence, the rest of you would be obliged to fill congressional seats... positions naturally unsavory to the sane and honorable."

Thorax

While the Navy has attempted to be systematic in naming its ships, in recent years it seems there has been a complete breakdown in any attempt to sustain a systematic practice in the name categories for ship types. The first ship named for a living person was USS Carl Vinson (CVN 70) in 1975. Other ships named for living people include:

• USS Arleigh Burke (DDG 51)
• USS Hyman G. Rickover (SSN 709)
• USS Ronald Reagan (CVN 76)
• USNS Bob Hope (T-AKR 300)
• USS Jimmy Carter (SSN 23)

This lack of discipline in distinguishing between the quick and the dead has been utterly overwhelmed in recently years by the promiscuous distribution of names among various classes of ships. One of the chief benefits of the classical naming system that flourished during the Second World War was the precision with which the name of a ship defined the ship's class, no small matter with a Navy boasting thousands of ships. The elegance of the system in which battleships were named for states, battle-cruisers for territories, large cruisers for large cities and light cruisers for small cities is difficult to exceed. But as the 600-ship Navy has evolved into the 300-ship Navy, it would seem that a presumption has arisen that one should be on a first-name basis with each ship of the fleet, and that no further introductions should be required. Half a century ago, there would be no doubt that a ship named after a state of the Union was a battleship, whereas today a ship with such a name might be whatever class of ship found favor with the Navy at the moment. This situation has reached absurd proportions with the SSN-21 class, the three units of which are named after a denizen of the deep, a state of the Union, and a President. This problem is not entirely an esthetic one, though the esthetics are the matter are difficult to ignore. As the Navy is increasingly called upon to operate in a joint environment, the services's increasingly confusing ship nomenclature will only compound interoperability problems [indeed, one may wonder how many Army and Air Force personnel are aware that there is, in principle, some system by which the Navy names its various ships].

http://www.history.navy.mil/faqs/faq63-1.htm

All the way, sir!!!

Aircraft carriers were also named for former Navy ships, i.e., Enterprise, Hornet, Ranger, etc.

Steve is right.  Ships are named after the lead ship of that class.  For instance, the Reagan is a Nimitz class carrier and all of that class are named after important military/political figures.  I think for the amphibious assault ships they still use the names of Marine battles, i.e. Tarawa, Iwo Jima, etc., but how they decide what the name of the lead ship of a class is I don't know.

Only two defining forces have ever offered to die for you, Jesus Christ and the American GI.  One died for your soul, the other for your freedom.

"History teaches that when you become indifferent and lose the will to fight someone who has the will to fight will take over." COLONEL BULL SIMONS

It's open season and everyones got a favorite! Some compare it to trying to name your kids!

"Let's Go Downtown" - Flight of the Intruder
 

http://www.327infantry.org/second/c_co 

Same Mud Same Blood - NBC documentary filmed 1967 RVN, chronicle Frank McGee