What organization could one work for that gives free or discount travel to its employees?

Airlines, travel agencies, cruise lines

Hotel companies do as well. Several of the large chains offer an employee discount or complimentary rooms when not travelling on business. We could be on business travel to another location, book the flight for an extended stay over the weekend, which would save the company money on a cheaper flight. Then we would book a stay at a hotel on the employee discount program and pay for leisure expenses out of pocket.

There are many other jobs have similar perks tied to travel, e.g., sales people, professional speakers and consultants, inspectors. The problem is that extensive travel is not glamorous, and most road warriors just want to be home for any time off.

I think REI, Patagonia..Also travel magazines must get their content from somewhere. And companies like Anthropologie seem to be doing extravagant photo shoots abroad all the time.

The U.S. Navy
U.S. Air Force
Marines
U.S. Army

Journalists, both photo and regular.