If I change to synthetic oil, does that mean I don't have to change oil until every 12,000 or 15,000mi.? I think that's what BMW's maintenance schedules are.

 

You might get away with that. Personally, I change every 5-6K or so, even using synthetic.
If you stretched it beyond that, you would definitely want to look at the oil quality- and not just the oil level, when you check the dipstick. (and make sure you use a high quality oil filter)

 

While you can probably get good results using premium synthetics for up to 25,000 miles you will be voiding a portion of your warranty since the maximum recommended change interval is 7500 miles. You also need to observe the every 6 months schedule if you are not putting a lot of miles on your car.

BMW's service interval is determined by the ECU and is dependant on how you drive, a lot of highway miles in top gear will let you go farther than a lot of around town driving. I don't know their exact algorithym but I think it is both rpm and throttle position dependant and probably has a time out as well.

I'm using Amsoil and changing every 6 months even though Amsoil claims I could go a year. I'll probably only put 6 to 8 thousand miles on it a year.