I work for a Fortune 500 company based in the US.
My company has a simple travel policy: Travel within North America or within Europe is always on the cheapest coach fare, and intercontinental is business class. Travel has to be booked through the corporate travel desk.
There is a little bit of slack in these policies; if prefer Delta, for example, and it is $10-$20 more than the lowest fare, they are generally OK with it. Interestingly, they are always OK with Southwest -- it generally assumed that they are the cheapest, even though that is often not the case any more.