For a holiday, it would definitely be at a travel agents, I would hate to book something so expensive and important online, there is too much leeway for an error occurring. At least if the travel agent is making the booking, at least this is what they are trained and paid to do, and gives me a bit more peace of mind.
If I were to book for a concert, or music gig, I wouldn't mind booking online, as this is sometimes the only way to get your tickets before they are sold out, and sometimes you literally only get a few minutes to buy your tickets for massive sell out concerts.
I've had really good success with airline tickets online. In fact, one friend of mine has her mother call me when she plans her little adventures with "the girls" - they are all in their 80's! If I were planning more than just a couple of nights in a hotel somewhere, I would definitely book through an agent and get a full itinerary, etc. As Diane pointed out, they are paid to get it right.
As in most things, I prefer to do it myself online. I never use a travel agent. Even though I may not be as efficient or good, I feel I have more control over my own vacation when I do it myself. This carries over into most other things in my life, too. I believe I can do a better job, and get a better deal, because this means more to me than it would a travel agent.
I would love to buy tickets online because you find so many great deals! But (like most things) when you do not live in the USA it is not so easy because in a lot of sites they ask you to be a US resident, have a VISA credit card, etc etc etc.