So I discussed the thing with a friend of mine that's been shooting motorsport events for quite a few years now and here's what he's got to tell:
To get decent panning, you have to:
1. get a long lens - something from 100mm up should do. If you only have something like 18-55, then sorry, but it's going to be very difficult unless the cars go really slow.
2. try to close the aperture a bit (when it's bright and sunny, then it's not a problem, aperture priority will do it on its own). It should help with getting the whole car in focus, though you should not rely on it too much and expect it to be that much helpful.
3. instead of going for continuous shooting, try to have 2 or 3 shots, focusing between the shots themselves (or if you have a good AF performance, just stick to continuous AF and it should do with continuous shooting).
4. be patient and try until it works good for you
I've had at least 200 or 300 attempts and never got anything really good.
I will try it this week during a rallycross event in Poland :] Hopefully there's something to share with you after the weekend:)