I don't know what it is, but it showed up in my yard about 3 years ago. At first I thought it might be some kind of wild geranium. Like you, I thought it was kinda pretty so I let a patch of it grow (pulled up as much as I could of the rest to be on the safe side). I can tell you that it makes no burrs or spikes, was evergreen last 2 winters, but it doesn't flower either - at least not obvious flowers - but if it doesn't flower to make seed I'm not sure how it made it into the yard. It doesn't creep or crawl, but the clumps do seem to get larger (by undergroud roots maybe). It might make a nice groundcover, but I would consider it to be invasive cause I am pulling up clumps of it all over the yard all the time. THe roots don't alway come out when I pull cause the stems break off. Sprayng is my next plan of attack.

Actually that was identified in your first post as Bowlesia incana.

OK, now I feel silly. It was the first post and somehow I totally missed it! I really thought no one had gotten that. Thanks for helping me with this!