Sedum
There are so many species of sedum it's hard to keep track. These guys are our favourites. They are ground covers and if left to their own devices, they would take over the joint. We use primarily two different types: Blue Tears and Green Ice (no, we're not making those names up).
Origin: Mediterranean
Hens & Chicks
Aren't these the best?? Although they are not native to our country, certain species are perennials that can be planted in your garden. They can act as a form of ground cover, if you're patient. They spread by releasing their offspring or "chicks" that roll away and sprout roots where they land.
Origin: Southern Europe and Northern Africa