Where can I download the flight plan data around the world, so that I have analyze their route?
Are they provided freely?
For historical FAA IFR flight plan data, you can get it from www.flightaware.com. They show five minute delayed, and with a free registered account you can get access to the last 90 days worth of data. You can pay for data older than that and I believe in different data formats.
I'm not aware of a similar source for other parts of the world.