The main "uses" of the Doppler effect are, as other people have already mentioned, in the measurement of velocities. In addition to police radar, it's used in weather radar. That's why local news stations (at least in the US) are forever touting their "Doppler N" (for large values of N) weather system-- those systems use the Doppler effect to measure the speed of water droplets in clouds, which provides additional information about their composition and nature.
I can also confirm that they use the Doppler effect in ultrasound imaging of the heart, to measure and map out the flow of blood in different regions. Before my daughter was born, they thought she might be at risk for heart problems, so we had a pediatric cardiologist look at it. They have a nifty color-coded display showing blood moving toward the imager as blue, and away from it as red. (That was the second-best part of the whole thing, after the doctor giving her a clean bill of health...)
My own research area is in laser cooling, where we use the Doppler effect to ensure that atoms only interact with light when they're moving toward the laser. If you tune the laser frequency slightly below the frequency the atoms want to absorb, a stationary atom will not interact with the laser, but an atom moving toward the laser will see the frequency shifted up, closer to the resonant frequency for the atom, and will be more likely to absorb light. When an atom absorbs a photon of light, it gets a small "kick" in the direction the photon was headed. If the atom is moving in the opposite direction to the photon (that is, toward the laser), then the "kick" will act to slow the atom down. With the proper arrangement of lasers, you can slow atoms down in any direction they try to move, thus reducing their overall velocity. Since temperature is a measure of the average kinetic energy of the atoms making up a sample, slower velocities mean lower temperatures. You can easily reach microkelvin temperatures this way-- a few millionths of a degree (C) above absolute zero.
There are a lot of complications along the way-- the Doppler effect is both the key to laser cooling and a problem that needs to be overcome in slowing atoms from room temperature-- but that's the basic idea. There's more information, and nifty Java applet video games, at the Physics 2000 site at the University of Colorado.
Laser cooled atoms are the starting point for all manner of experiments in atomic and molecular physics, and quantum optics. The most important technological application at the moment is in the area of atomic clocks, with the best cesium atomic clocks in the world using laser cooled atoms. At various times, there have been suggestions to put atomic clocks in space, potentially as a next generation GPS system, which would improve the already impressive precision of GPS navigation. I'm not sure what the current status of those ideas is, though.