The airlines are the most reputable to deal with and you usually don't save much at all by going to a 3rd party. The airlines don't provide them with much of a discount. If you read the fine print on the 3rd party sites you will see that they don't have to have any capability of providing you tickets at the prices quoted.
3rd parties have to compete for tickets from the airlines. They don't maintain a stock of seats themselves. You request the seat and they go and get it for you... but you are not guaranteed the price that they initially quoted. They base that price on what they could have gotten if the inventory was available.
Some of them also add on service charges and have significant change and cancelation fees.
If something goes right and you do get an ultra deep-discounted ticket from a 3rd party, and a flight is late or weather happens, expect to be the last priority the airline has to re-seat on an available flight.
One of the other things we've seen happen is that some 3rd parties cobble together tickets from non-associated airlines. Say you want to fly A to C, but you are connecting in B. Sometimes a 3rd party will sell you a ticket that includes a ticket for A-B return and another for B to C return. If the A to B flight is late and you miss the B to C flight. Congratulations. You are stuck in B unless you buy a new ticket, at last minute prices.
We usually recommend to use Kayak or skyscanner to identify the airlines that fly the routes and then go directly to them to get the ticket. CHasing a little bit of savings can cost you a lot in the end.
Edited: 10:09 am, February 02, 2012