US PPL valid in other countries?

[mattpilot]

Hi there.

I was wondering whether I, a US PPL holder, am allowed to fly in countries like Germany or Austria (Europe).

What limitations, if any, apply to me. And what rules/regulations apply?

Lets say it would be possible, and i would go to europe on my next vacation, could i just go to an airport, rent a plane, and go fly or would i have to fill out some gov't paperwork?

Last question; Generally speaking, what are the major differences when flying in the US and when doing it somewhere else?

Thanks for any help!