If you want to stay somewhere and not pay anything at all for accommodation, try couch surfing. There are various sites on the web, mostly, but not exclusively, aimed at the younger end of the market. Usually you're required to contribute in some way - sing and play an instrument, cook, garden - but by definition it doesn't involve money. I was a couch surfing host when I lived in Hobart, Tasmania when my son was young, and we had many delightful guests.
Hearing people's stories was a way of travelling without travelling.
If you're happy to do some work in exchange for food and a roof over your head, try WOOFing or conservation volunteering. Again, there are many sites to choose from. Usually a set number of hours' work is required, then the rest of the day is yours. The positions are often in rural places you may not otherwise see. Be careful though of people who treat WOOFers and backpackers as a source of unpaid labour and give little in return. This is not a labour contract in any country, and you are not required to stay if conditions are inadequate. Friends have told me about being poorly fed and housed, right through to the other extreme of being treated as part of the host family.
There are also sites for people looking for assistance with a wide variety of jobs, such as house renovation and gardening, in cities. They work on the same basis as WOOFing, but are suburban.
While we're talking about working in other countries, if you're under 30 it's possible to find work as an au pair. Ideally you're treated as a big sister or brother. You are housed, fed and given "pocket money" in exchange for helping take care of children and some housework. This is opening up in countries like China, where people want their children to learn English. In places where housing is expensive, such as London, having housing as part of the package is a definite bonus.
Country hotels often employ bar and restaurant staff and provide housing too. In this case you need a work visa as it is a "proper" job. In areas where these businesses are seasonal, it can be a great way to see places otherwise hard to get to. In Australia special work visas are available for people who are prepared to work in remote areas. When Julie and I drove across the Nullarbor last year we were often served by people with interesting accents who were working at the road houses hundreds of kilometers from anywhere.
If you're prepared to plan ahead, do a course in teaching English as a foreign language (TEFL). I know people who have taught in many different countries and have had some great experiences. Some jobs are short term, such as over the summer months, but most schools require a commitment of a year. Some of the summer jobs are for live in schools, and teachers are expected to live in as well. Remember to check on working visas before leaving your home country. TEFL jobs have a wide range of pay rates depending on country and school. Countries such as Vietnam and Finland value teachers highly and pay well.
I'm currently working as a cook/housekeeper in Bournemouth. While I could have probably found employment in my former career of accounting (which I didn't really want to do), this way I don't have to fit out an apartment, I get to join the family for dinner each evening, and I'm cooking again in a well fitted out kitchen. I've missed cooking, and don't enjoy cooking for just myself. I take two lovely little dogs for a walk beside the sea every afternoon. I get paid for all this, which, having done all of the above for nothing for most of my life, is a minor miracle.
And I have the added bonus of having time to write the blog and work on my next two stories!