This topic is a hot one. My previous job was as a travel consultant for one of the largest travel consulting agencies in the world and I have traveled to over 22 countries in the past 8 years, and have booked travel using every method possible.
The truth is, it really depends on how much time and effort you are willing to put into planning your trip. Planning and purchasing something as simple as a round trip flight online could not be easier and I highly recommend it to save money and time. It requires very little information and thought. Travel agencies charge for their service, and that charge could be between $20.00 - $200.00, depending on the flight and destination. As well, there is nothing that the travel agent can provide for you that the internet cannot.
If you are planning a larger trip, with multiple destinations, internal flights or tourist attractions, booking online could be a bit more work. Having said that, it is still not that hard. It is just a matter of doing your research. If you are planning a trip to Spain and are planning to travel on to Italy by boat afterwards you would simply have to search the information on busses or trains for your overland travel in Spain, and the ferry information for your boat to Italy. Sometimes you are able to pre-purchase your internal travel or tourist attraction tickets online, sometimes you can take care of it when you arrive at the location.
However, if the research is something that you do not have time for, or you feel a bit more secure having your trip planned by someone who does this as a profession, a travel agent may be the answer for you. They have the ability use a plethora of travel resources and their experienced co-workers, but this will come at an extra cost for their service.
Here is an example of a fairly large trip I planned as a travel agent. Two clients of mine wanted to travel to the UK for 3 weeks. They asked me to plan everything from international and domestic flights to the hotels and travel insurance. By the time that this entire trip was booked and paid for, the clients ended up paying roughly $500.00 more than they would have online. As a travel agent in this particular company, as with many companies, you are expected to mark your products up, and are penalized for not doing so. The clients did not see this mark up as it was hidden in the grand total.
Everything that I planned and booked for these clients could have been booked online. As a travel agent I had access to a few cheaper hotels than they would have found online, but as a travel agent, I was expected to mark them up! The security of having them reserved and paid for when they arrived was worth it to these senior citizen travelers. Travel agents are not rip off artists, but it is part of their job to "mark it up".