Airline flight crews, military, photo or print journalist, nature photographer. The people that do the most travel in the company I worked for were supplier management people - particularly auditors. With globalization, a lot of supplied parts, materials and subassemblies come from far flung places around the world. Some of the people I used to work with traveled to Germany, China, France, Mexico, the US, Korea, the Czech Republic and other places around the world frequently. One of the most in demand fields anywhere would be healthcare - it's the one area where you would be most likely to be able to land a job in a foreign country if you're interested in that. In that case, your job may not directly require travel, but you may be in a position to go out exploring on your own on weekends and holidays. I lived in Italy for the last 13 years before retiring and had the chance to visit most of Europe during that time.
You need to be aware that traveling for a job is not the same as travel on a vacation; it can be a great opportunity and rewarding. It can also be a lot of wear and tear - you really have to have the right personality to be on the road a lot and you don't necessarily get a chance to spend any time sightseeing. You could also consider foreign service (i.e., diplomatic corps) or the volunteering with the Peace Corps.