NO! I used to, until they screwed big time. I ordered a ticket and Orbitz sent me a confirmation. I checked the airline ticket two weeks later only to find that I never had a ticket. I called up Orbitz and yelled at them an hour, but the best they would do is give me my money back in the form of a voucher +$150 (instead of just giving me cash). They didn't even send me the voucher until much later, so I had to pay for another ticket (that now cost $150 more).
When you use third-party sites, you are not actually buying a plane ticket. You are paying Orbitz/Expedia to ask the airline for a ticket. If they don't get it, they usually let you know immediately and don't charge you. Sometimes it gets messed up like in my case.
Using one of these sites is okay if you are ordering a ticket long in advance. If not, you're going to be in trouble when you find out that you didn't get your ticket and prices have skyrocketed.
Now days, if you are only buying a plane ticket, there is absolutely no reason to use these sites since airlines usually guarantee that their prices will be cheaper (usually by a few dollars). Use a site just to find which tickets are cheapest, then order the ticket through the airline directly.