I've had my '97 540i for about 18 months now--bought it with 68K miles, and now has around 110Ks...pretty heavy use.
Generally quite reliable. I've had to replace the cooling system at a cost of $1600 at around 80K mi. Cooling problems triggers strange electrical problems (like one headlight not working, some warning messages showing up in German, etc.) but once the cooling system was replaced, all's well. But I believe this is more of a V8 issue.
I've had serpentine belt come off on the freeway a few months back, but that was a minor repair. But had to have it towed, so it was a hassle. Also replaced battery, brake pads, etc...normal stuff.
Otherwise no unusual problems. Not a rattle heard inside, even after 110k miles. Pretty solidly built. How BMW can manage to have the car ride so nice when it handles so well is quite amazing. Paint/finish holds up quite well...people don't believe that my car is a '97..they think it's brand new!
'87 560 SEL
'97 BMW 540i 6speed
'00 Lexus LX470