That is quite the difficult and controversial question. Before I answer, let me say that tax law is not my area of expertise, so you should consult a tax professional about your personal situation. Another better source than me about this is Tax Help for Gamblers by Jean Scott & Marissa Chien. Chapter three deals with this topic.
The general rule of thumb is that earnings are taxable and gifts are not. So a no-obligation comp would not be taxable. Anything that was given to you based on points, a drawing, a tournament, or earned some other way would be taxable. Granted this is not going to cover every situation, and some situations can be in a gray area. If you’re in doubt, consult a tax professional.
This question was raised and discussed in the forum of my companion site Wizard of Vegas.