Sedum spurium 'Green Mantle' is another fast growing ground cover for sun or shade. It also has lovely pink flowers in the summer.
Two-Row Stonecrop (Phedimus spurius 'Green Mantle')
Sedum 'John Creech' is another
Two-Row Stonecrop (Phedimus spurius 'John Creech')
There are others that would make great ground covers depending on the growing conditions.
Some very small leafed ones that are beautiful once established:
Sedum makinoi 'Ogon', Sedum makinoi 'Limelight, Sedum makinoi 'Variegatum', Sedum lydium and the list goes on. Some show their best color in sun and others need some shade to do well depending on what your summers are like.