Make sure if your going to be camping you get your International Camping Carnet Card
, This will give you access, privlages, and discounts on campsites all over the place. You can get it from your local AAA.
Here is a link so you can check the info, and see if its for you...ICC Info
Hope that helps ya some, and the answer to your question... Yes you can camp through europe!!!
Most of the camp grounds have showers and laundry for you to use, as well as a place to stock up on supplies. M
Most of these camp sites will be out of the city center, so expect to pay for transport into the city to sight see.