Jai - it's a mix of what all these people have said.
If you have an FAA licence and are flying an N registered aircraft (standard cert not experimental) then you may fly anywhere in the world subject to respecting the local procedures and applying for overflight or landing clearance when individual countries require them.
Local procedures vary slightly from place to place but everything is pretty much standard if you fly IFR.
In the USA, Canada and most of Europe you don't need specific overflight clearances - in the middle and far east you generally do. These must be applied for in advance, in writing, with the relevant authority.
All these things change if you are flying a locally-registered aircraft in another country (or outside its state of reg) so you have to be more specific!
So if you fly your US registered aircraft into Canada you are OK - the only paperwork you need to do is with customs and immigration. Once you are inside Canada you may fly at will.