They're great cars, really...and when you actually break it down, they aren't very expensive to maintain at all.
The most common problems on those cars are, in no particular order:
-Valve cover gasket leaks
-Oil pan gasket leaks
-Vanos oil supply line banjo bolt on back side of oil filter housing loosens slightly
-crankcase ventilation valve goes to shit, requires replacement of CVCC and all hoses
-Lower control arm bushings/ball joints fall the fuck apart (every 100k or so)
-Radiator expansion tank crumbles and goes to shit, lower radiator hose coolant temperature sensor leaks
-Power steering hose clamps leak, need to be replaced with regular screw-type hose clamps
And really, for the most part, that's it. All of those are going to happen every 100-150k or so. As far as services, every 10k or so you'll need to change the oil and/or do a 'Service 1', 'Inspection 1', or 'Schedule 1' (Depending on who you ask - Inspection 1 is the proper term) - which is really just a glorified oil change. I charge $160 for an Inspection 1. From time to time the vehicle will call for an Inspection 2, which is the same as an inspection 1 buy adds air filter/cabin filter/fuel filter and spark plugs, in addition to the oil change. The maintenance computer will vary the exact mileage by your driving habits - it's average for a 'from new' vehicle to call for its first Inspection 1 in 15-18k miles and then an Inspection 2 at around 45-50k. I charge $325 for an Inspection 2. Typical 'Dealer' charges are $300 for Inspection 1 and $650 for Inspection 2, most independents charge about a hundred bucks less than the dealer.
Outside of that, you'll need to do a transmission service every 60-70k or so. BMW shows the transmission fluid in theses as 'lifetime' fluid, but people forget - as far as BMW is concerned, the 'lifetime' of the vehicle is only as long as their warranty on it. These call for a fancy fluid, which is really just Dex III. I use synthetic Castrol Global Multi-Vehicle ATF when customers opt for non-OEM fluid (which, literally, IS Castrol synthetic), however I use the Castrol stuff in my personal vehicles. Just like BMW OEM synthetic oil, it's Castrol. I charge $275 for a transmission fluid/filter/pan gasket change. Some people have issues with them leaking after a fluid change, but that's because you didn't torque the pan right or you didn't use an OEM gasket. That's another thing - gaskets. You HAVE to use OEM gaskets on these vehicles. HAVE to. Anything else WILL leak.
Outside of that, they're really good and really reliable cars. The 5 series has a bigger chassis, so there's a lot more room around the engine than in the smaller 3 series...they get mid-20's MPG, depending on the condition of the car and your driving habits. There can be some quirky issues with the interior wiring, but the 5 series didn't get the MOST bus bullshit until 2003-4, so the E39's are still a relatively easy system to work on. There's a lot of voodoo 'woo woo scawwy' stuff floating around out there about changing out the stereo systems, but I have no idea why - I've got aftermarket speakers being powered by the factory amp with an aftermarket head unit that were all just plug-and-play; in place of the factory head unit is an Alpine single din, with an OEM BMW Euro single-din radio bezel. I'm also running a cheap-o Fusion powered sub that I got off of eBay that's tapped into the factory amp.
I've got cheapo eBay coilovers in the front, and stock self-leveling airbags in the back that I modified the height sensor links to set it lower. I made a black tip and powder coated it and welded it on; I painted the exterior trim black and put an aftermarket eBay cheap-o M5 front bumper on, and replaced the headlight lenses with $60 aftermarket lenses, and at the same time installed new eBay headlight adjuster arms (this was actually kind of a pain in the ass). Wheels are Concept Ones with spacers to sit the wheels right...and that's pretty much all I've got in the car. I picked the car up for around $1400 or so, may have been a bit more, I don't really remember...fixed some body damage, got it running, did some catch-up maintenance, and now I've got around 220,000 miles on it, and I drive it daily and take it from Houston to Dallas every single weekend. Gets 24-25mpg on the highway and is an all-around comfortable-ass car to drive. I think I've got less than $4500 in the whole car, including buying the car.
I don't think you can even buy a fucking Civic with clean interior and decent wheels for 4 grand.
I did the interior in textured 3M carbon fiber vinyl on Friday after I shut the shop down for the weekend, took me about 3 hours but it came out pretty damn perfect - other than getting the weave the wrong direction on the console. Easy fix though, I'm going to wait and see how this holds up over the next few weeks before I re-wrap any of the pieces. This is the first thing I've EVER wrapped, and I didn't watch any how-to videos or anything...just got after it the way I thought it would work best.
The day I bought it:
Best fucking car I've ever owned, and also the cheapest. I will NEVER sell this car.