I've been recently experiencing this problem, so I will impart some of my knowledge to you.
I don't get shudder when accelerating or decelerating, just when braking. This means, that the Upper Control Arm bushings need replacing and indeed, mine do and as a result, the car tends to wander a bit all over the road. Polyurethane bushings are the better way to go as they are more stiff and apparently last longer than OEM replacements.
http://bmwe32.masscom.net/ - Under "Fixes --> Suspension and Steering --> Upper control arm bushes"
Upper Control Arm Bushing
If I did get shudder when ac/decelerating, then I'd be looking at a sticking caliper as the most likely cause, which I think I might have anyway due to a sort of "grinding" noise that's more noticeable at city to highway speeds.
http://bmwe32.masscom.net/ - Under "Fixes --> Brakes --> Brake Caliper Rebuild"
Brake Caliper Rebuild
Then there are the cars that you'll never be able to get rid of the problem despite having to replace the entire front and rear suspension and driveline vibrations...