I, personally, tend to use the airlines directly. At least then if they screw up my booking then I can go to a desk and sort it out at the airport on the day of travel. I don't much fancy being stuck on the phone while check in is closing behind me, as I've seen happen countless times.
Of course if you book with a good, solid, reputable agent then you will usually have no problems, in deed I often check them first and now and again their prices are too good to turn down. Complex itineraries using airlines across multiple alliances or airlines which aren't aligned are a lot easier to book with agents, no doubt.
Some of the online only ones, however, even the big names can cause major problems and fail to deliver on their promises or totally misinform people. I've lost count of the number of times "cheapoholidays.com*" have sent people to the wrong terminals at airports, or totally lied about baggage allowances and seat allocations!
I don't always think the agents are the cheapest option either. Recent personal experience showed me that a package being offered on a popular online agency (which was being advertised as the cheapest deal) was almost £30 more per person than booking the whole trip directly with the airline and then booking the exact same hotel on their website directly.
*not a real travel agency