I work for a smaller company, so we make all our own arrangements and aren't required to use anyone in particular. So I agree with the others - either go directly with the airline or use a real, reputable TA for work travel.
I almost always book direct for plane tickets as I usually book refundables anyway and only fly AA/OW. There have been times when AA.com hasn't been able to book a fare I know is available. I've always been able to tell a TA exactly what I was looking for and they were able to book it for me. A good TA can really help out if things get ugly too.
I haven't found any advantage to booking through a place like Orbitz. Fares are pretty much the same and you may have to pay a fee to use the service. If you have to make a change, a lot of airlines won't touch it unless you pay a fee for them to take control of the reservation. They'll direct you to the site normally.
Hotels I always book thru their website or call the property. If you don't go thru an official channel, Hilton denies elite benefits. Can't speak to others. Most rates don't require you to pay up front, so it can make cancellation easy if your trip changes. Also if you're inside the "cancel with penalty" window, you can call the property directly and plead your case. I've gotten out of a few now show fees that way when my plans changed. Places like Orbitz will generally show you the advance purchase price, so good luck getting a refund or making a change. That price will often match the website anyway.
I only book thru National for cars as I like their Emerald Aisle. Usually get coupons and such via email so I book direct. Emerald Club is one of the most convenient programs out there. Again, no charges until you pick up the car, so cancellations are easy.
About the only time I see an advantage in using a site like that is if you're going to buy a package deal. You may be able to save some money that way, but that's really only good for personal travel.