Boeing, most routes are an attempt to achieve the shortest distance between two points (Direct GPS) however in the real world for various and many reasons this is not the case.

The first and most obvious reason being that most if not all of the air routes around the world were designed on earlier great circle navigation and then had little bends or changes in them because they were all based on ground based navigation aids and you tracked via VOR or NDB from point to point along a route from A to B, except on long over water route segments. Geography had a lot to do with where you could actually get a VOR or NDB sited on the ground and so some of them have ended up in what seems like funny places because you had to get in an out to fix them or do maintenance on them by road or similar convieniance.

Second, There is also a rule about distance from land for various types of aircraft, except 4 engined aeroplanes, to allow for diversion to a nearby or nearest airport or to keep you within a distance in a one or two engine out configuration that also led to some funny routes that you see. Working this out is quite complex because of different aircraft performance specs, speeds and altitudes and general winds aloft etc for an engine out configuration and generally you will find on charts of routes that most of this is already built into the route structures. To give you an example, in Australia the longest non stop route was Sydney Perth or vice versa. Most airlines and aircraft except say a long range 707 could not legally do this and maintain the required statutory fuel reserves required for the flight (727 etc) so you would plan Sydney-Adelaide-Perth get over the top of Adelaide recalculate the fuel remaining and then do a slight of hand because you now only needed a smaller reserve for the remaining distance and go on your way to Perth without stopping, however if the winds were really against you and boy they could be some days, then you could land at Adelaide and refuel.

Third and probably most realistically, routes into and out of major cities are also structured to keep inbound and outbound aircraft seperated for Air Traffic Control purposes. So you tend to go one way departing and another arriving. You can generally pick this up from the route charts as they will put a little arrow on the air-route indicating the direction in which it is intended to be flown. Terminal charts tend to show this more clearly. Then having said that you could always try you luck with ATC and ask for inbound route going outbound and if the traffic allowed you might get it somedays, anything to save a few air miles and the precious fuel burn.

Then their are geographic or sovereignty issues where in one country won't let you fly a certain way because of defence or military reasons, so you end up with another strange dogleg around some point or place on the earth. Kamchatka in the old USSR was a case in point, go there or near there and they intercepted you and shot you down no ifs or buts, ask the Koreans they lost a couple like that.

So it has handy for simming to have the charts to look at and not just rely on the electronic software to do it for you. For the US the FAA publishes a broad scale chart which was for ATC purposes but is available free on their web site along with other charts. Trouble is the charts are designed to be printed on large scale plotter printers not your A4 printer so getting them dowin into sections you can print off at home is a chore!

Hope this helps explain some of the ins and outs of air routes.