I have a 1993 530i. Today I had the AC going with the fan speed set to 3 (of the 4 settings) and the fan abruptly stopped. The light on the AC button stayed on but no fan blowing. I turned the fan speed thru all 4 settings and the only one that works now is the fastest (#4).

Any ideas?

Sounds like the limit switch for your fan speed has gone bad, they generally default to high speed. It is commonly known as a "sword". Most e34 5 series and e32 7 series cars have these and are they are interchangeable with each other. There are lots of rebuilt ones with warranties on ebay for about $100.00 (dealer=$$$$). I put a used one from a 750iL in my 535i and it's worked great for 3 years so far. Replacing it is kind of difficult, you have to pull the glove box for access and it's mounted towards the center of the dashboard, but it's well worth the effort. You also might want to change the cabin filter since you're right at it. Good luck.
Mike
1989 535i 5-speed
Yorktown VA