The basic point to get across is that first and foremost it is the
State of Registry of the aircraft that detemines what papers are required to fly it (and also what regime it is maintained under).
If you have a license issued by the state of aircraft registry then you can fly worldwide (private flights only; commercial ops are a different can of worms).
In some cases, the state of registry permits additional concessions. For example the USA allows its registered aircraft (N-reg) to be flown (outside the USA) on any license issued by the owner of the airspace in question. So e.g. if you have
no US licenses, you can fly an N-reg in Mongolia if you have a Mongolian issued PPL. To fly it in Germany you would need a German issued PPL (and a UK issued JAA PPL won't do - I have the references if anybody wants them).
These additional concessions are fairly random; there is no rule to them.
The state of registry of the aircraft basically controls what is needed to fly it legally. That is the ICAO treaty. On top of that, the owner of the airspace can impose additional requirements, or impose limitations.
As to what you can do with a plain PPL... well quite a lot. You are stuck to VFR rules only (clear of cloud, basically, and in most cases clear of controlled airspace) which limits weather flexibility and routings, but the potential is limited only by how much time and money you are willing to throw at your competence and your aircraft's capability. I flew down to Spain and Crete, VFR. Well, usually VFR
but let's not go down there