That is the holy grail for travellers!
It turns out there are quite a few opportunities but the ones acceptable and suitable depending on what you are willing to do and how much you want to make doing it. The real difficult part is getting paid well at the same time as you travel but I do know a handful of people who managed.
Let's see what other answers come up with but here are some that I know:
- Cruise Ship Crew: Just this week Disney advertized to find people to work on their cruise ships. What you get is room and board, a basic salary and long shift work for months at a time, usually without any days off until you get time off for a few weeks. The schedule and destinations will vary but you get to see many tropical countries.
- Cabin Crew: Same principal as a ship crew but it requires lengthy formal training and detailed background checks. The pay can be very good with the perk of seeing one or two different places per day. You can get a reasonable number of days off and take then at different locations around the world, depending where your airline flies.
- Tour Leader: Companies that lead tours need leaders to run the tours, take people from place to place and communicate with local contacts to ensure the trip runs smoothly. You typically lead a few different tour around the same area, repeating the circuit every few weeks. Travel expenses, room and board are covered as is a nominal salary. How exactly it works depends on how tours are run. GAP Adventures for example asks the leaders called CEOs (Chief Experience Officers) to pay upfront a few before being trained to lead a tour. After a certain number of months passes, you get the deposit back. You can to know certain places very well and have funds for living in between tours. You can also run your own tours, as I used to do, but that is more erratic. It takes a certain number of participants to make the tour viable, so tours often get cancelled due to not having enough participants, at least until yours become popular. My friend Jim Cline manages to do this very well with a number of successful tours happening every year.
- Customer Relation Officer: You can be paid well to visit customers around the world working for companies that produce products and services used internationally. I used to work in Video Effects and some people (not me, those with PR and Marketing skills) spent considerable time visiting video production companies and special effect houses from America to New Zealand. Another friend is now working for a major software company and goes to interview customers several times a month in different countries.
- Installation Specialist: Again this is a skilled work and I know know to people who managed. One covered nearly all Central and South America by going to install banking software and customize it to the local regulations. Here you spend a little more time at each location, often a few weeks and head back to the home office. Another friend has to install hardware controls in flight simulators to make them match the make and model of each aircraft. Doing so involves visiting pilot training centers usually around the head offices of airline company.
Not so applicable but worth considering:
- A few years ago, there were lots of Voluntourism. This is when you join a specific community and teach then or help with something. It could be as easy as teaching a language, installing software, computer parts and networks or hard manual label such as helping with a farm. It eventually got so popular that these place more-often-than-not ask volunteers to pay a non-trivial amount the opportunity! Usually room and board is taken care of but conditions vary greatly.
- Language Teaching The most popular is English. You do not need an education degree but certificates greatly help. The issuer of those has connections to places that require tham. This is a good opertunatly to know local culture but you usually will not be traveling so much. Classes are 3 or 4 months usually, although a longer obligation is asked for those that get training included in the preparation. Pay can be reasonable and sufficient to live in the local economy.
- Creating Your Own Job: Write reviews of anything travel related. Rachel Lucas for example focuses on The Food at each destination, getting paid travel and high end culinary experiences. Could be text reviews, articles (Matador pays something rather small for accepted travel articles and photo essays), videos about a place or an aspect of it.
There are seriously much more possibilities. You must have the necessary skills, suitable work visa (if the hiring company does sponsor) and be apt and able to perform the duties. Some are much harder than others.