For many years I ran a 23 on the rear and a 20 on the front, with no real problems and in fact still have two of my bikes set up that way.
On the two I ride most, however, I've gone back to 23's front and rear, just so I don't have to change so many tires around, so often, i.e. a slightly used rear becomes the front and the new tire always goes on the rear (but hey, that's just me).
Rick / OCRR