Go to www.stepables.com and check out the different ground covers for your requirements. You might try Mazus or the Pratias or in shady areas golden creeping jenny - lysmachia nummaleria aurea (spelling this from memory so may be faulty) does well in part shade in our area. Also Vinca major (periwinkle) does very well. There is a lovely variegated periwinkle that I've grown in quite dense shade, but it will do just as well in sun from what I hear.It has a sweet little blue flower that comes twice a year. Ajuga (bugleweed)can be a lovely shady ground cover there are some variegated varieties that include pink in the color mix and they bloom with a purple flower spike.
Personally, I'm fond of the creeping jenny you can create fabulous effects by having bulbs grow up through it.
Laurie