Do you need a travel agent?
Like all answers to life's major questions, it depends.
Chances are thay you probably won't need an agent if you are to book a flight from New York City to Los Angeles and spend less than a $1,000 on a weekend trip to Ocean City.
Things change when it comes to more complex trips or very expensive ones, where you might not feel comfortable charging the family credit card $12,000 over the Internet.
Fodor's Guides has a good online article discussing the merits of (still) having and using a travel agent for your travel plans.
I would say, you could pretty much anything you want online, to include booking a multi-city vacation to Europe, but you still need the comfort of being able to talk or contact a human being who would be able to guide you in the right direction.