When we approach a wave (or the emitting object approaches us), we INCREASE the speed with which the crests pass by us, there by increasing the frequency, or shortening the wavelength. For this reason, it is also called blue shifting.

When we move away from a wave (or the source emitting the wave moves away from us), we DECREASE the speed with which the crests pass by us. This decreases the frequency (increases the wavelength). For this reason, it is also called red shifting.

Mathematically, the Doppler Effect is described in this way:

Lambda is the wavelength of the light, delta-lambda represents how much the wavelength has shifted, and c is the velocity of the wave.

You can see from this equation, unless the velocity between wave emitter and wave `listener' is some reasonable fraction of the speed of the wave (c), the wavelength shift will be imperceivable. This is why you can not drive fast enough in your car to make a red stop light turn green!

Fun with animated gifs! Below are some movies showing objects moving at differing speeds. Mach 1 means its traveling at the speed of sound.

1) Stationary Source
2) Source going Mach 0.7
3) Source going Mach 1 (Bullet going Mach 1)
4) Source going Mach 1.4, supersonic! (Bullet going Mach 1.4)