Secondary air pump went out at 105k. Part was 350 USD, and not from a dealer, but was relatively simple to install, taking around an hour to complete the job.
Water pump went bad shortly after I got the car. With its plastic impellers, these parts have been known to fail. I replaced it with a better quality one, also changed hoses and thermostat.
Rear wheel bearings went out about 3k ago. This was the only time it has been in a shop, since I bought it. It seemed quite labor intensive, and required special tools. In the end it cost around $500 to fix.
Radio deck had a power issue. It would come on and off, and repeatedly ask me to enter the anti theft code. This was dealt with by purchasing a new Alpine deck, that cost around 200 dollars off of Crutchfield.
If you like to drive enthusiastically, I HIGHLY RECOMMEND reinforcing your sub-frame.
Previous to this, I had a 98 Audi A4 2.8q. The Audi was a very good automobile, and shared a number of good traits with its German counterpart, however, the 328i is much more dynamic and fun. They are both about the same size and weight, but their personalities couldn't be more different. Though one could argue that the design of the BMW is slightly more archaic, the build quality of the BMW is far superior. Whereas the Audi felt as heavy, if not heavier than it actually was, the BMW feels like a lighter car. The steering is fantastic as well, and best of all, (when compared to the Audi) no electronic gremlins to speak of!
One thing you notice right away, is that this car is built for the autobahn. It is far and away the best highway car I have ever driven. It's athletic and eager to pass, excellent at climbing up hills, and feels unbelievably planted. Many people will be quick to say that this is a great car for your favorite mountain road, and don't get me wrong, it most certainly is, but the freeway is where the success of this car is most unmatched.
Another thing I prefer about the BMW, is that it is far easier to perform repairs on than the Audi. No timing belt headache either. If you are mechanically inclined, you should look no further.
Interior has held up nice. The leather in the back has gotten a little brittle with heat and sun, but then again I hardly ever have a rear seat passenger. Glove box won't close all the way. This doesn't bother me, because it shuts, there is just about a centimeter-wide gap between where it sits and where it is supposed to be. The headliner started to come undone in the back, but I re-tucked it, and it has held up fine. The car smells very nice inside, and I don't use an air freshener, because I'm allergic.
The paint and exterior look new, though the car is now 13 years old. A tree branch did fall on the hood, and caused two tiny little dents, but it still looks good, and I get comments on the (fern green) color all the time.
This car doesn't get bad mileage either. I have never averaged less than 20mpg. And I primarily drive it in the city. On the highway, I have gotten over 30 as well. The trademark BMW analog MPG gauge really helps, when you are looking for good efficiency.
I am sure this car has some drawbacks. If you take it to a shop, repairs are expensive, but there are some really good DIY articles out there, and the online community is the best I have ever experienced. People that drive these cars really love these cars.
The best thing about this car is also its biggest downfall, and that is the double edged sword of affordability. Don't get me wrong, I love the fact that I got this car for about 5 grand, but I hate nothing more than when I see one of these cars, strapped with a fart can exhaust, and ugly Altezza lights. This is a classy car that is now commonly raped with cheap aftermarket accessories. Yes, all of these cars were created equal, but their owners were not.
So it is especially imperative with these cars that you find one that has been maintained and fixed/modded the right way. You will be rewarded, and nothing but happy with your purchase.