why aren't there nuclear powered aircraft?

Nuclear power is the only way to make submarines work underneath the water for long distances without coming up because of the oxygen that all other types require.

And batteries for electric engines are too heavy.

Historically a submarine had to go up to just below sea level to get air through the snorkel for the engines that charge the batteries.

Then it could go down and drive only as far as the batteries could get and then repeat the process. But because the batteries are huge and heavy, this is only a short distance.

Under water the diesel engines do not work, they need the oxygen out of the air.

This was a huge disadvantage at war times.

Nuclear power does not need the fresh air (the oxygen part of it) like all other types of generators that work with combustion engines, which need oxygen. So someone built a nuclear submarine and this was so superior to the old ones that they chose to do it. They can travel and hide for months without coming up.

Some military ships are also nuclear powered:

http://www.radiationworks.com/nuclearships.htm

It allows them to travel longer distances without refueling.

For civilian ships it is probably too expensive.

For air planes it seems easier and safer and cheaper, compared to nuclear power, to just power them with kerosene. A reactor is heavy and has a certain size. Large ships can carry them.

Submarines and ships have unlimited water cooling available.

Needless to say, there is no idea too crazy not to have tried in the 1950's, see for example http://en.wikipedia.org/wiki/Project_Pluto and http://en.wikipedia.org/wiki/Aircraft_Nuclear_Propulsion .

To elaborate on Thomas's answer, there was serious research put into it, before the advent of good ballistic missiles: https://en.wikipedia.org/wiki/Aircraft_Nuclear_Propulsion

The idea was to build B-52 type planes that could just loiter in the air in an undisclosed location for a month, which would eliminate the risk of a Soviet first strike taking out the planes on the ground. Basically the same tactic as a ballistic missile submarine: Hide With Pride.

The basic principle of operation was the same as a jet engine: pull in air with a compressor fan, heat it, expel the now-much-higher-pressure air through a turbine which powers that compressor fan. But instead of heating air by burning jet fuel in it, they would pass the air through the core of a nuclear reactor.

It theoretically would have worked, but the project was killed because ICBMs mostly solved the same problem better. And also a crash would have smeared nuclear fission products across a wide area, which would have been expensive to clean up. It's a very interesting project though. To keep the vehicle light enough to fly, the radiation shielding was only between the crew compartment and the reactor, so the plan was to keep the plane in a radiation-shielded hangar when not flying. The plane never flew though.