I have a pulley that I removed from my car. I probably should have done some more research before I actually removed the pulley. How can I tell if that pulley is in fact bad?
In the absence of specific information, here are some general inspections that you can try:
Does it turn at all? Most automotive pulleys should spin fairly freely without noise. Otherwise, you're going to have a fairly miserable driving experience from all the shrieking parts.
If this is a load-bearing pulley, check the axle: is it straight? Does the pulley rotate on a fixed center?
When attached to the engine, does it spin rapidly? Did it burn out its bearing? Look for evidence of discoloration or general gook on parts that should be clean.