cpham, the basic rule is that you can only do two things with motion: you can choose to freeze it, or you can choose to show it. If you use a fast enough shutter (at least as fast as the object is moving in terms of time) you can freeze the motion at that instant. You can also choose to use a slower shutter to show the motion blur, or you can even exaggerate it by using an even slower shutter and showing more blur. As a rule of thumb, don't try anything slower than 1/60 sec without a tripod, or the whole picture can become blurry due to camera shake.
A cool (but tricky) thing to try is to set the camera to a relatively slow shutter speed and "pan" the camera while the car is driving by. That basically means that as you take the photo, you follow the car with the camera while trying to match its movement. What that does is it blurs the background and keeps the car relatively in focus for a neat effect. You have to be good at following the subject though and keeping it in the same spot in the frame or it will become blurry.
This is an image by professional photographer Ed Kashi titled "Saigon on Wheels" (1994) that shows the result of panning the camera to follow a moving subject:
So basically it all depends on what you want to do. Do you want to freeze the cars and the background? If so, then keep the camera still and use a fast shutter (or even follow the object if your shutter is sufficiently fast to not blur the background). If you want to show motion blur in the cars, but not the background, then keep the camera still and reduce the shutter speed. If you want to blur the background and keep the cars in focus, then move the camera with an appropriate shutter speed for however much background blur you want.
I haven't really experimented much with panning, but I imagine it's tricky to do... especially if the object is moving really fast, or if you have trouble moving the camera steadily without shaking it. Maybe you can practice it on cars driving by on the road? Start at 1/125 and move down to 1/60, 1/30 etc. gradually to get a feel for it. A tripod will help, but it also makes it more cumbersome to follow the moving object. Try different things and see what works.
Of course, you're limited in what you can do by the amount of light you have to work with. If you're trying to stop fast motion, it's probably in your interest to use a higher ISO setting with a fast lens... or at least make sure to go when there's adequate sunlight.
(By the way, these are general techniques that I know of. I don't know how much of this applies to race car situations. If anything, I think you'll probably end up having to use faster shutter speeds than what I quoted because race cars are pretty damn fast :P)