Plenty of info posted on this lately if you'd do some searching.
Having said that, there's no problem with going to 16, 17, or even larger. When you increase the diameter of the wheel, you use a lower profile tire to compensate, with the result being that the overall wheel/tire package is the same diameter as the 15 wheel/tire package.
Go to
http://www.tirerack.com and enter your vehicle data. They'll show you what wheels they have that will fit your car and they'll tell you what size tires you need for the size wheel you pick.
Most of the other tire sites on the net do the same thing.
This site has a good size comparer calculator that shows some good info on the effects of various wheel and tire combos, i.e. how much your speedometer might be off with a new package, how much closer you might be to the suspension or fenders, etc.
http://www.rims-n-tires.com/rt_specs.jsp
Oh, and pay attention to the offset and bolt pattern on the wheels. Not just the diameter. Of course, you probably already knew that since you indicated previous wheel/tire experience