Powering Arduino with reverse car lights?
It depends very much on the car and your Arduino. There are two factors to consider:


Leeching power off lights can have an adverse effect on the car's ability to sense a blown bulb.
Many Arduinos have a 2 second delay while the bootloader executes (some even have 8 seconds).


If your car doesn't sense blown bulbs (most modern ones now do, even cheap ones) and you can work without a bootloader (programming directly with a USBasp for example) to avoid the power-on delay, then it may be possible, yes.

As has been mentioned by others, using a switching regulator is the best method for powering the board as it avoids excess power loss through heat (which can especially be a problem in confined spaces). I would recommend not using one of the cheap eBay modules, but instead using a proper "cigarette lighter" to USB adaptor (available from all good gas stations priced $5) which is designed to work with automotive voltages. A car's 12V power has transients in excess of 50V sometimes (back EMF from the spark generation) and the electronics have to be able to cope with that - those cheap eBay modules aren't designed for that and could die taking your Arduino with it.