As said above it comes down to two things... Your ability to do the research and your ability to know what you are getting yourself into as a traveler. If going out of country, this exponentially can make a situation worse if you do not know what you are doing. If you are not an experienced world traveler, definitely go with an agent to arrange everything if you travel overseas. If you aren't an experienced travel shopper and know plenty about where you are going within the country, still use a travel agent. Travel agents often can make sure you not only have a good place to stay (not luck of the internet), have everything you need, but they can also point out what you should see and do there within your interests (so you don't just get there and spend half the time trying to figure out what to do ... pre-plan). Never think something is as simple as just getting plane tickets there and a hotel.
That said, I do not use a travel agent. However, I have traveled enough over the years to generally know what to expect in different types of travel or how to get the correct and appropriate information. If I were going someplace completely foreign to me, I would probably find a travel service that specialized in that location to make sure I had an easy going trip.
The last part.. This is your honeymoon. It is incredibly important to the person you are marrying. No matter how much you know or think you know, getting the best travel agent should be your preferred route. Vrai mentioned Carlson above. I also recommend American Express Travel Group.