One thing to be careful about on Priceline's name your own price: Make sure you read the times. If you schedule a flight on say, July 6, the plane can leave anywhere from 5am that day to 2am on July 7. You do not get to see what the schedule is until AFTER you pay, that is the catch. Also, you might pick a price of $400, but taxes and fees can easily double that. You get to see the price before you put your credit card information and pay though, so look at the price, then do a regular Priceline search and compare prices. The prices you see on a regular search already include taxes and fees.
Priceline's name your own price can be a huge bargain provided you know what to watch out for and you know the caveats.