Le Paper Globe: a do-it-yourself terrestrial globe
joachimesque.com
joachimesque.com
your ancestry/family tree overlayed?
travel logs?
historic airline route maps?
Early explorer journeys?
WW2 troop/invasions?
starmaps?
Can it be done with hexagons and pentagons like a soccer ball? It may get more rounded, but probably harder to assemble.
For dramatic effect, consider a pop up shape such as http://numberloving.com/tag/dodecahedron/ (easy to make) or http://www.mathmos.net/misc/popup-icosahedron.html (tricky to make it pop up reliably)