I have never saved one penny with mine, but I don't really travel that much. As far as I know, you can't really save money on flights, but some hotel chains do give you a discount, maybe 5-15% off rack rate.

A co-worker did once use his card to get reaccomodated onto another airline after a nasty schedule change. The agent didn't want to do so and tried telling him she couldn't, so he pulled out his card and said "I know for a fact that you can, so get me on their flight immediately." She did it.