WH - this is a big subject and if I may say so has been all over the internet for years now.
The various parts of the legislation have been gradually working through the EU drafting and parliament. I don't know how much of it is in place now but probably enough...
You can find an overview
here which I think is reasonably up to date.
Basically, EASA is working towards requiring everybody flying in EU airspace (regardless of aircraft reg) to have
EASA pilot papers, IF the
operator is based in the EU.
The nationality or residence of the
pilot is not relevant.
What or how "operator" and "based" will be interpreted, nobody yet knows, and there seem to be obvious work-arounds for corporate/bizjet ops, but if you take the simple case of an EU resident owner pilot then there doesn't seem to be an obvious way out.
ICAO still requires the pilot to have papers from the State of Registry so if you are flying an N-reg you need FAA papers.
The duplicate EASA papers which are proposed to be required are in most cases not even going to be valid for that aircraft, but that doesn't prevent the EU forcing this. They are entitled to require the pilot to carry a taxidermy competence certificate.
The requirement for the duplicate EASA papers has been postponed till April 2014 - for UK based pilots at least.
Various conversion routes have been proposed, some of which are well defined while others (like the one for getting an EASA IR from an ICAO IR) are working their way through the system and nobody is sure what they will look like.
The full EASA PPL should be ICAO compliant.
The EASA LAPL won't be ICAO compliant (due to the GP medical, etc) and each EU country will need to file a difference to ICAO if they want it usable outside the EU. Non EU countries will therefore be entitled to reject it.
Who the EU is going to screw is not hard to work out, but their actual objectives are opaque and apparently wholly political. There is
no safety case for any of this.
For FAA PPL holders the conversion to an EASA PPL is not hard - so long as they can get an EASA medical. Those who cannot, and cannot use the LAPL (e.g. because there will be no IR or IMCR on it) will be shafted for good - unless they move to the IOM or the C.I.
For FAA IR holders the conversion is not yet defined.