Within busy areas like Europe and the USA routes taken daily by the same flight may vary due to traffic, weather or other reasons. Eg Airspace may be closed for military exercises. I have known traffic from London Area airports bound for Spain and Portugal to fly out over the Atlantic initially because of problems over France. Routes flown from Europe to the USA depend largely on Atlantic weather systems. One day a flight to Los Angeles may fly over north Scotland, next day it may fly over Northern Ireland or even much further south.
Once you get into busy terminal areas everything is radar controlled so there is every chance that on two consecutive days the routes taken by a particular flight may be completely different. For example, at very busy times aircraft which normally route to a particular holding area may be re-routed to another where there is less traffic.
It's more complex than that but that should give you some idea..