We've experienced a wide variety of them throughout our travels, such as going to a family's house for dinner in Nassau (you can see our host family as well as us doing the dishes above). We learned more in that one sitting about the country and the way its people live than we did in the rest of our four days on the island, and it wasn't scary or hard to come by. We just signed up through the tourism board, who arranged all the details.
While having dinner at someone's house is a common people-to-people offering, each country has their own take on the idea of connecting tourists with locals. Some are free, like in the case of Nassau, and others come with a cost, such as the "home restaurants" of Estonia (Mermer, for example).
In Sweden, a company called Mication is serving up a slice of Swedish life in Malmo. All the programs are a little bit different, but all accomplish the same goal: Putting the traveler in direct connection with the people of that country.
This sort of tourism is one we can really get onboard with because it provides opportunities for people of the world to connect with one another (keep in mind that just as you are being exposed to them, they are being exposed to you!). The programs are truly good for anyone and everyone, from solo travelers to families. In the case of the latter, you can arrange to hang with a family who also has kids approximately the same agea really cool way to get your kids comfortable with diversity around the world.
Be sure to check in with the tourism board of your next destination to see if they offer any similar opportunities. Trust us! The pool will still be there tomorrow, and we guarantee it will be the most lasting memory of your trip.