These days, I book either directly with the airline (for domestic flights) or via a travel agent (for my complicated overseas work travel). I have in the past been screwed by exactly the situation that mivadar describes, which is why I don't use Web booking sites for anything except searching for fares. Orbitz/Expedia can be very aggravating to deal with on any irrops issue, and the carrier will refuse to make any changes on an agent-issued ticket.

That said, JerryFF's point about having a travel agent that you know personally doesn't always do much for you either. I like my travel agent well enough, but she is not at work 24/7, and since I do a lot of overseas travel, many of my re-routing snafus tend to happen when her office is closed. I get routed to the "after hours" service, which is some faceless call center God knows where. Inevitably, they are completely clueless and take hours--if not days--to get the problem sorted out. Not fun. Sometimes it just makes more sense to book directly with the airline, at least if your routing is on a single carrier.