Does my Apple TV bought in America work in european countries? Like Spain and Portugal? Does the video format change in anyway? Or will everything work just fine?
Yes it will. I use an American AppleTV in a Latin American country and it works just fine as long as your TV have the required HDMI input.
However the content your AppleTV will show varies from country to country, as the iTunes catalog of Movies and TV Series is region specific. You can check what movies and series you will be able to buy or rent using Tunes on your computer. The same content will be available on your AppleTV.
You also might want to try Netflix if its available there.