There can be a lot of things. A full catalyst, old oxygen sensor,  the airmass sensor, or like the mechanic sad, you have to clean the fuel injektors but you should do it professional and not just poring some aditiv in to your car.
Maybe it is just a little air hose that is displaced at it is nod providing enough air to the air and fuel system.

I took the car to BMW and after two hours of labour charges.  They said they found nothing.  The computer showed up nothing and everything looks fine.  Unfortunately, the problem is still persisting and now there is also some speradic hesistation when I excelerate.  I hit the gas and there is some slight hesistation and then it jerks forward.  The stalling with the brake is still happening.  It may happen twice in a day and then not for a couple of days.  My fear is that it will happen at a stop light and someone will be on my tail and I will be rear ended.

Not sure what to do from here.  It's very frustrating.  I am think of just packing in the car and getting something else.

Any other words of wisdom?

if your car also hesitates when accelerating, check the 02 sensor, this might be the cause of the problem

if you're really so worried about it, make sure you have your hazard-lights on and apply the brakes if you think the car will stall.
Otherwise, just don't drive the car with your kid in the back... or use another car (if available).
Good luck with the problem, hope you'll get it fixed.
Keep us up to date, and let us know what was wrong (then we can help others with the same probs)

I have a 1995 325I also I am experiencing slight hesitation but its very intermittent, I know its scary, it happened to me the first time June 7th on a major freeway now it like once every week. I changed spark plugs and checked coils and wire connections for deffects this weekend then will go for the fuel filter next if it continues, then as the other postings say sensors vacum hoses etc. until I find the problem....man what do you expect its a Bimmer the ultimate money machine!

Here is the lovely update.? We are going on day 4.? Yesterday they finally found the problem.? The bottom line is $1500 which sounds very rich.? The thing I find baffling is they keep saying that nothing showed up on the computer.? Did they even bother to go underneath the car and check it out.? I would think an oil leak would be fairly obvious, but what do I know.

We have traced the fault to the ignition coils.? We found oil residue
leaking into the ignition coil causing the stalling/misfiring. This oil leak
also contaminated the spark plugs.

At this point, we recommend replacing the valve cover gasket to correct the
oil leak $290 labour & $80 parts,
Spark plugs $108 parts, 6 ignition coil $70 labour & $840 parts.

Please let me know if we may proceed.