How to get a "classical" globe projection

This family of projection is called azimuthal orthographic (all rays from globe to flat map are parallel). You can define the Lat/long coordinates of the center of the projection to choose the visible hemisphere.

There is no EPSG code from what I know, but here is the PROJ.4 definition.

+proj=ortho +lat_0=Latitude at projection center 
            +lon_0=Longitude at projection center
            +x_0=False Easting
            +y_0=False Northing