Can you use a 500mA 12VDC transformer on a unit that requires a 180mA 12VDC?

From your question I assume you are referring to a charging adapter for a piece of electronic equipment. I believe adapters also contain a rectifier that rectifies AC voltage to DC. The one I'm looking at at this moment does this.

Your thinking is correct, in that any thing that transforms the voltage to what you need is all you need for that step. But if your adapter rectifies the voltage you will need a rectifier with your transformer.