Do transformers obey Ohm's Law

Yes, they do.

The confusion for most people comes from the fact that ohm's law says that when voltage goes up, current goes up; but conservation of power says that when voltage goes up, current goes down.

The reason it still applies is that a transformer divides a single circuit into what are actually two electrically-separate circuits. Ohm's law applies to each sub-circuit individually, while conservation of power must hold for the entire circuit as a whole.

A more in-depth explanation can be found on this page: http://www.blueraja.com/blog/194/do-Transformers-obey-ohms-law