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No one has mentioned lamium. I planted it years ago as a groundcover because I liked the leaves with light edging and yellow blossoms. I don't think I could get rid of it if I wanted to, because every year I pull it out of the iris and other perennials and every spring it is back smothering them. Creeping Jenny could be a problem, but hasn't become one yet. Most groundcovers are by nature spreaders, hence invasive.
I agree with the post on liriope; I can't get rid of it, either. Or English ivy, which comes into the backyard from neighbors on three sides. On the other hand, morning glories never reseed for me and I wish they would!