No AC, system has a leak.
Automatic headrests don't work (easy fix though).
Various instrument lights are burnt out.
Diagnostics computer works intermittently (does not affect driving).
Developed the dreaded 55mph shimmy (mine was strut related).
Transmission is becoming temperamental.
Climate control system acts up (vent selection).
Drive shaft center link needed replacing.
Aux waterpump fell apart (bypassed it).
Radiator replaced.
Aux cooling fan motor fell apart (re-glued the magnets).
The car is a pleasure to drive.
It has very beautiful styling, especially if you have the m-par wheels on it in chrome.
The interior feels very roomy and is very comfortable.
It may be showing its age now, but when compared to the 3, 5 and 6 series of its day it holds up best in the looks department, mainly due to the wide kidney grill, which I believe was only available on the 1993/94 740i (L) series.
In my opinion the e38 styling was also very nice, and then the 7 started to look like less of a car.
Performance wise, it's a heavy car and at 286hp the power is adequate. While off the lights you will have no problem eating up the Honda's, some of the new cars sporting 300+ hp V6's will give you a run for your money. But racing off the line is not where this car shines, it is a pleasure to pass cars on the highway, no matter the speed you are at, when you need to pass, she won't let you down.
I also mentioned comfort earlier. A 7hr drive is no problem. Bring a catheter and you'll only have to stop for gas, which by the way isn't that bad if you're coasting on the highway. But bring it in town and you'll see the needle dive quickly.
These cars are getting hard to find in good shape, but if you do manage to get one then you'll get to drive quality and not some Ford.
The typical older BMW: cheap to buy but costs the same to maintain as a new one, which is why you see so many old BMWs around that could be charitably described as hoopties.