Mike, I got another one!
Galium odoratum, or sweet woodruff, is evergreen for me. I think it dies down in colder zones. I can give you some to get you started if you end up coming to our fall plant swap. They spread easily but aren't invasive in my experience.
You can use the leaves for teas or fruit drinks, although I've never tried it myself. It's also used to make May wine, which I'd love to try, but I've never seen it anywhere. Hm. I just realized mine didn't bloom very well this spring. I wonder why.
Oh, just thought of St. John's wort as I was typing. Hypericum calycinum, or creeping St. Joh's wort, is evergreen for me. It's the only Hypericum I grow, so I don't know about the other species. St. John's wort is technically edible but it's medicinal with quite a few contraindications. I've read that you can make mead with its flowers.
