I take quite a lot of flights for both business and pleasure, and although I typically book my business flights through a (corporate-mandated) travel agent, I always book my personal flights directly with the airline (I should add that I am fussy, and I normally fly only with full-service airlines; no budget ones for me).
From time to time, I read that booking flights through a travel agent, either online or physical, can lead to cheaper prices. At least for simple trips (one airline, maybe a simple return), I have a hard time believing this to be the case; the airline has most direct control over their tickets, travel agents add a layer of extra indirection that has to be paid for, etc.
So am I losing anything by not booking with a travel agent? Am I really likely to get better prices?
Edit: I should be clearer - let me restrict the scenario by imagining that I already know what I want - e.g. to get from LHR to ORD on date X/Y/Z, with no stops, ideally on American Airlines. Can a travel agent still offer me something in that scenario?