belts, fan clutch, radiator hose neck... Not too much that catestrophically fails in BMW's rendering them undrivable, but it does happen.
These wont cause it to fail but will make the handling\experience worse:
Get the car on a lift and check all the bushings (control arms, rear trailing arms, swaybar, etc etc etc) Odds are, they are probably worn all to hell and need replacing. That can really revive the handling of the car more than any other upgrade if the bushings are worn out. Get under the car with the mechanic or buddy and examine what he's doing and how the undercarrage looks. I wish I could have done that right when I got mine, gave me a really good understanding of it.
If your wheels are squeeky at all, you probably need a new wheel bearing.
Search the forums\google for E36 common problems and check them out.