Yan Holtz shows how to draw great circles using an R package called geosphere:
This post explains how to draw connection lines between several localizations on a map, using R. The method proposed here relies on the use of the gcIntermediate function from the geosphere package. Instead of making straight lines, it offers to draw the shortest routes, using great circles. A special care is given for situations where cities are very far from each other and where the shortest connection thus passes behind the map.
Now we know how to make pretty-looking global route charts.