Are you certain? For the past decade I have noticed that transatlantic flights typically have a moving-map display of real-time position and ETA that shows when there is no movie playing. I always pay attention to those maps when I fly from the Western US to Europe. If they are not great circle routes, they are pretty damn close.
Polar routes are often great circle routes; the two are not mutually exclusive. A great-circle route means that the shortest distance between any two spots on the Earth's surface lies along the line defined by an imaginary plane through those points that also intersects the terrestrial sphere in such a way as to divide it into two equal halves.
The Equator, the ecliptic, and each meridian line of longitude are examples of great circles, but there is an infinite number of great circles of varying angles of incidence and points of intersection. Any line that divides the globe into two equal halves is a great circle.
You can find great circle routes by yourself with a globe and a shoestring. Stretch the string over the surface of the globe between your origin and destination. If you do this between, say, San Francisco and London or between Paris and LA, you will be surprised at how far north the great circle will take you. That's why you can see Baffin Island and Greenland and Iceland out the plane window. It will also show you why aircraft landed at Goose Bay and Gander in the days when they did not have intercontinental range.
Perhaps you are mistaking a great-circle route for a rhumb-line route, which has been little used since the days of sextants and astrolabes, or a "small circle" defined by lines of latitude other than the Equator.
-ccm