A Private Pilot can act, as pilot-in-command or co-pilot of any aeroplane engaged in non-commercial flights. In other words, you can take passengers on every airplane on which you are qualified, but not for remuneration. Your licence allows you to fly all around the world.
Different other qualifications exist to expand your flying skills as well as your privileges:
Instrument rating, to allow you to fly in all weathers…
Aerobatics, for those of you who have a strong stomach…
Seaplane rating
Glider towing, parachute dropping…