voltage regulator, leds

The LM2937 is a great regulator for automotive use, but is overkill in your situation.  A typical 7805 will work fine and provide years and years of troublefree service in an automotive environment (if used correctly).

What the LM2937 offers that the 7805 doesn't is a low drop out voltage (completely irrelevent to your application) and low quiescent current (again completely irrelevent to your application).

The drop out voltage is how much higher the input has to be then the output for the output to stay regulated.  Typically, in a car, you go with a 5vdc output so as long as you have more then 7vdc on the input (ie battery) the 7805 will be fine.  The quiescent current is how much current the regulator itself needs to operate.  Since you won't be leaving your dash lights on for extended periods when the car isn't running a few extra mA (typically 6-8mA) of current draw isn't going to hurt you.

With any voltage regulator the proper procedure for running it is to select the component (say a National Semiconductor LM2937ET-5.0/NOPB) and then download that specific data sheet ( http://www.national.com/ds/LM/LM2937.pdf).  If you look at page 8 of that data sheet it will show you the typical application - follow that diagram and the recomendations closely and you''ll get great results.

The LM2937 has special considerations due to it's low drop out design and the capacitor calculations can be cumbersome (especially in colder environments).  Unlike the 7805 if you don't have the correct capacitance on the LLM2937 the output can oscilate and damage whatever is hooked up to it.  The colder the climate the more capacitance you will need to prevent the oscilation.