Sure. In my case it was friends of family, and family of friends, sometimes a little distant but people were welcoming enough. Those were the best because you could stay a while and they were more relaxed with you, they usually wanted to show you around their town etc.

Also, sometimes I stayed in hostels that were small, family-run, more like a home than a hostel. So you saw the family life there too.

And some families rented out spare rooms. You used to meet people at a train station or other travel hub and size them up (does this happen now?). Sometimes get recommendations from other travellers going in the other direction. Important to note I wouldn't recommend this in general, particularly if you're female or travelling alone. And it requires a good deal of careful judgement and experience. I don't think I'd do this alone.

Maybe Airbnb makes this easier and safer nowadays. I've stayed in a lot of spare rooms in the US via Airbnb and had similar experiences.