In looking at replacing my disc brake rotors, and looking online I see there are different sizes available (between 180 and 203 mm). My question is, what dimension do I measure on my existing rotor? I'm assuming it's the outside diameter, but just want to be sure.
Yep, it's the diameter. Most likey 160mm, but double check. You'll need to get the same size rotors as your old ones unless you get new adapters for your frame.
Also, different manufacturers produce rotors of differing widths. Magura rotors tend to be around 2.0mm, while Avid and Shimano are around 1.8mm.