A flashing landing light can be used to acknowledge a light gun signal, it can be used to signal a communications problem (but they would also put a certain 'squawk' in the transponder). On some planes, they automatically flash on/off for collision avoidance.
Other lights you'll see on aircraft are position/navigation lights (steady red on left wingtip, steady green on right wingtip, and steady white on the top of the vertical stabilzer trailing edge).
Anti-collision strobe lights generate white flashes on each wingtip and at the most aft point of the fuselage. An anti-collision rotating beacon is located on the top of the vertical stabilizer and has a red flashing light.
And many aircraft have separate landing lights and taxi lights (both of which are white lights). Many landings lights can not be used on the ground for too long due to overheating, hence taxi lights.
Edit: typo...