Agreed about travel agents. I recall when working for a small consultancy, our contracted agent booked me 'fully flex Y' because she thought it was cheaper. I had stated that this trip had fixed times and I didn't need flexible. I discovered that it was more expensive than a discounted C. Fortunately, that was just to Switzerland.
Best agent was when working in the City in the late 80s. We were such a big company, that we had a whole branch of AmEx travel IN thebuilding. So you got to know the staff and they they you. They followed our instructions and the policy of each individual department - there was no blanket stricture, save for F and Concorde.
I have been an employee of minor to major (i.e. global corporations) with small consultancies and self-employed direct to the client. It was very rare for there to be a sensible policy. Working directly for clients was the worst as you were already considered over paid. So, naturally I went 3/4 way round the globe in five days (inc work for one) in Y and was expected to be in top form, 12hrs after landing in HKG!
On countless occaisions, I have travelled the night before and paid the hotel out of my own pocket, rather than get up at 04:30 to make a 09:00 in (say) Paris. I recall dozing in a taxi and waking up, staring out the window to try and work out where I was, the answer was Paris. Even just driving to MAN to be fresh in the morning, can be worth a night stop - depending on what you have to do the next day.
I agree with almost all the points made here, are you the Number 2 on the project, or are you the lead? Also, if you travel with a colleague, you WILL talk business and that can be highly beneficial to the company. Having an extra four hours (spread over flight/transit/dinner) can be very helpful, away from the hurly burly of the office - but it does not show up in the company accounts!