Certified 'mystery' and 'secret' shoppers can find job in any sector including travelling industry. You may not have option to choose the place, but you can go there for Free and get payment for easy work. For instance, you could have been one of the secret shoppers who flew around England and exposed discrimination against disabled passengers.
You need a good resume and references to find a gig like this. You will be given free accommodation in exchange of watering plants or walking with a dog or doing similar light chores and errands. You get enough time for exploring a totally new city.
If you have valid driving license, you can drive someone else's car across the country for free. This auto delivered service is called drive-away. You have to pay for fuel and some deposit. But car delivery services are much less costly than renting; especially when you want enjoy a cross border adventure.
Teaching can offer chance to visit almost anywhere in the world. It is one of the most rewarding travelling options. It also allows a chance to know other culture closely and meet lot of like minded people. Your travelling expenses are covered by the salary you get and many institutions in fact, pay the expenses.
If your history is good and you want to spend time in a place, know about the place and apply for a tour guide position. Most specialist tour companies, hotels and tourism offices recruit English speaking persons who have knowledge in local language as their tour guides. You need to be smart, confident and charming to be a successful tour guide. It is a good though bit hectic way to travel long trips for free and earn money in addition.
International flight attendants often have to spend a night or a day in a foreign country. They also get huge discounts on their personal flights. For getting a higher remuneration think about becoming a pilot.
Usually this needs commitment for months, but offers lot of benefits including free medical & dental care, transportation, food & lodging and attractive remuneration.