I've had a bunch of K series bikes including a low-mileage K100RS 16V that I bought crash damaged and rebuilt, 110k K75S and a ~50k K1100LT. They have a couple of breed-specific problem areas that can cost major money but those are easily sorted if the bike has been looked after well. Gearbox input shaft being the main one, you have to occasionally lube it with a special lube otherwise it'll wear. Repairing the damage will mean a gearbox strip down and that's either a lot of work or expensive or both. On the pre-paralever bikes you also want to grease the driveshaft splines on a regular basis (yearly IIRC), but that's not a massive job. Oh, and for $DEITY sake change the fuel filter - a lot of people forget that (it's in the tank and a bit of a PITA to get at). The K1100 had a fuel filter that had done about 50k. It didn't let that much fuel through anymore. ABS is good to have and generally robust, but people manage to break it because they can't be bothered to change the fluid. The four pot Brembos on the later ones can seize if the bike is layed up for a long time. You can get rebuild kits, at least over here, but they're not cheap if you need a replacement caliper.
Other than that, a K that's been looked after properly will go on for mega miles. Service intervals are 6k which is great if you ride a lot (I do), consumables aren't that pricey and a lot of the work can be done by a competent DIYer. The only reasons I have my BMWs (I've currently got an R1150RT that I bought with 25k on the clock in Nov 07 that's now showing 61k) serviced by a pro is that they're a commuter/business tool for me and as a freelance programmer no show = no money, so they have to work.
K series are very well balanced so you don't really notice the weight unless you chuck them into the scenery. They manage the same feat as the Honda ST1100 - as soon as they're rolling, the weight disappears.
For long term ownership and all weather riding, my choice would be the K1100LT. It's got superb weather protection, with the above caveats the drive train is bullet proof and they can easily cross a continent or two before breakfast without breaking a sweat. Well, once you put a better seat on.
If you want something more sporty, the RSs are a good choice, as is the K75S. The latter is probably the smoothest engine of them all (they've got a balancer shaft, the fours don't) but they're using the same amount of fuel as the bigger ones, they're just a little less powerful. You probably won't notice in normal road riding though.
None of these are sports bikes though, they're sports tourers at best and built for people who like to go from A to B, preferably via C and D, where A and B are a few hundred miles away.
Oh, and the golden rule of BMW buying - never buy one without at least side bags.