There are tons of way to travel with little to no money.
If you don't want to work at all, your options are more limited. Backpacking around with a strict budget will be your only option (if you can even afford to do that). Just be sure to:
1. Pick a place that is affordable. Europe is much more expensive than other parts of the world. The wealthier countries tend to be more expensive. In Asia, Japan, South Korea, parts of China, and Singapore tend to be pretty expensive. However, many parts of South East Asia are more affordable for backpackers (and as a result, are very popular for such tourists). Countries like Vietnam, Laos, Cambodia, and Thailand are among some of the cheapest (and generally safe) places to travel in the world. Just don't make sure you travel at the right time of year or the weather might destroy your experience.
There's way too much information to write here, so just do a quick google search for "how to backpack south east asia on a budget" and you will get a ton of resources.
2. You can work low paying jobs such as working at a restaurant or what not to fund your trip. This will give you the ability to live in one place and immerse yourself into the city you choose. When you grow tired, move onto another city.
3.. One of the most common jobs for foreigners overseas is to teach English. This usually requires a university degree from an accredited institution, though not always. Japan and Korea hire many Brits and Americans to teach English.
Do a google search for "teach english [insert country]"
4. Work at home and save up money for your trip. Probably the most "boring" ways to go about it, but if you save up beforehand, then you won't be stressed as much during your trip.
Right
Not legally. You would most likely be refused entry to most countries if you cannot prove that you can support yourself without working.
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