You made me curious. According to http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980225a.... there is no real connection between the direction of rotation within the Solar System and the Sun's orbit around the Milky Way. And again the Milky Way's rotation has little to do with its motion in the local group.
However across the Milky Way there are again a whole lot of things roughly moving in the same direction.
It looks like the Galactic Coordinate System (which, sensibly but to the confusion of the casual reader is centered on the Sun) is also 'backwards' with respect to the right hand rule. The galactic north pole is actually the galactic rotational south pole. This seems to be because the coordinate system was based on the rotational direction of the Sun.
I think I may have just exceeded my recommended daily nerdallowance of reading about spinning things in the sky.
However across the Milky Way there are again a whole lot of things roughly moving in the same direction.