That would be Priceline, but I believe it works a little differently than you think. You put in information about what type of flight you would like, times, etc. Then you put in the price you are wanting to pay and your credit card information. Then, it will search it's flights and if the site finds something in your price, then it will book it. Once it has been booked, you will then get to see what air you received. Now, that means, if you don't like the airline, time, etc. it will still book the flight and you aren't able to change it, it is booked.
I know that you are supposed to put in the air information that you are wanting and then it will only book flights that match that info. But just be aware, a lot of people have put in that information and the flight that was found didn't match what they wanted at all, but you are still stuck with the ticket. So, if you need a specific flight time, i.e. you are going to a conference or something, you may consider booking with the airline directly instead.
Hope this helps!
http://travel.priceline.com/default.asp?rdr=1