Not always, no, it depends on various factors, mainly the weather, flight paths change to avoid turbulence. Sometimes they also change to avoid congested areas, or areas that have become dangerous.
Flightdiary just puts the quickest great circle route, but flightradar24 actually uses live...
Another good site is Flightdiary , you can join up with your Facebook account and keep a record of your flights. You get them all shown on a map with the data. If you put in a future flight, you can tick a box and when it takes off it will post a message to your Facebook wall with a link to the...