Like several people here - corporate travel I must use an in-house TA. My assistant is able to a lot of it on the on-line system rather than through the actual people. She will get me a list of available flights around the time I want and then I pick the actual flights before she books them. She has a priortised list of who I want to fly (AA at the top, I won't even step on an AF flight) and all my FF numbers. We have the same system for hotels and the very rare car rental (I drove once in 2001 - hey, I'm from NYC). The on-line system will only let her book me on corporate approved airlines and hotels.
Personal - never, it's the internet for me.
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I Love New York