Travelling within Europe and stay with families has many advantages. The obvious one is the price, of course. It would be around the price of a cheap hotel.
Another advantage, and surely the most important one, is that you will discover the culture of the country or countries you are visiting much in depth than if you were staying in a luxury hotel or in a holiday village, for instance. Indeed, by staying with a family, you will experience a country’s real life and discover the local traditions.
You can find different associations which organise stays with families abroad, Servas for example, based on different criteria such as age, gender or even language connection. Beware you have to be a member of one of these associations to benefit from their programme abroad for a fee but then the board and lodging are free of charge.
Other programmes, such as Experiment in International Living (EIL), exist with no annual fee but then you do have to pay for board and lodging every time. The choice depends really on how many times a year you want to have the experience. In any case, there is always an interview of the family and of the travellers wishing to register in these programmes and also there are very strict rules about the length of the stay, etc., but everything is explained to you when joining.
You can find more information about these programmes in travel guides or, even better, check with the national tourist organisation of the country you would like to visit.
If you don’t feel shy, it is a great and unique life experience! Oh and just a little tip, it’s always nice to bring a little something to the host family when you arrive...