I would like to split a shapefile in qgis according to how the polygons overlaps. Don't know how to though? See pic for explanation:
I am more familiar with ArcGIS than QGIS but I just did a brief search and think this would work:
1) Use the Union tool (as suggested by Darren Cope) to create your 7 features.
Thus where there is only 1 original poly, the new field = 1, where there are 2 polys, field = 2 and so on.
I think I found a method. It s a grass function included inside the sextante plugin. See the screenshot. I did a test with a shapefile that looked like yours.