majenko:
The 78xx series of regulators are not a good choice for automotive applications.You should use an "automotive grade" regulator.
Voltage spikes on the 12V rails on a car or motorcycle caused by back-EMF from the coil / ignition system can reach voltages as high as 60 to 70 volts even when filtered. These spikes are about double the absolute maximum of the 78xx series of regulators.
Well the zener diode and L1 / L2 in the circuit above addresses the spike issue I think...