Rubus pentalobus / Rubus calycinoides sounds like a good match for what you're looking for.

http://davesgarden.com/guides/pf/go/81725/

Hardy, adaptable, and assertive but not invasive.

Cool, jordan; I'd never heard of creeping raspberry before.

I love snow-in-summer, but it really seems to be an on-an-off plant for me; good one year, not so good the next, super the next two, etc. Your mileage may vary, and it's super easy to start from seed.

My first thought was something like sweet woodruff, which I really love. But you say you have full sun? Under a tree?

Have you thought about some kind of sedum, like a stonecrop? the ones I've grown have proved pretty tough in Central Ohio.

Try to find sweet woodruff. I have it growing under my trees in my urban yard. It has white flowers in sring and loves shade.