In most European cities with a metro or regional trains, you can take one of the lines to the last stop, walk a few minutes until you get to a forest or fields, and easily camp. Just study the area first from Google Maps satellite, set up the tent late and break camp early.

It won’t always save you much money though. In some places the price of a regional train ticket out of the city and then back adds up to almost a hostel bed.

Also read about everyman’s right in the Nordic countries. You can legally camp anywhere outside cities. Everyman’s right is not really supposed to apply inside cities, but in the small towns foreigners can often get away with spending a night in a park.