For anything remotely complicated — or expensive — I use my travel agents, simply because in my experience they can often find options and deals that I can't, and they are more likely than I am to spot an anomaly in my itinerary and to mark hotel bookings for late arrivals, and so on. Also for the countries I visit there is often someone in their office with some local knowledge, which has been helpful a couple of times.

if I am booking a very simple — and inexpensive — itinerary, I sometimes book direct with the carrier on line and then book a hotel myself (usually by phone, in fact).

I'm not a big user of on-line facilities in this regard. Having said that, I do often look around before ringing my travel agents, but they have always matched and usually bettered what I have found on-line (in terms of cost, convenience or both).