I think it's a Tahitian Bridal Veil(Tripogandra multiflora). Does it ever have small white flowers that are held above the foliage a bit? I don't think they flower if they're given plenty of nitrogen, so you may not have seen any yet. If it's not, do a search for Commelinaceae family and after looking through a LOT of pics (*grin*), you'll find it. I'm just about positive it's in that family, same as most Wandering Jews like Tradescantia pallida (Purple Heart ~ aka Setcresia pallida ~ that purple one that everyone has), Callisia repens (Bolivian Jew), Zebrina pendula (that purple and silver jew everyone ELSE has), Rhoeo spathacea (Oyster Plant, aka Moses-in-the-boat, Tradescantia spathacea and Rhoeo discolor).
Know why they're called "Wandering Jews"? They practically can't die, so they're named after the biblical wandering jew who's doomed to roam the earth until Jesus's return. Neat, huh? :-) I love these plants, can you tell? LOL!
Wingnut, that is a very good possibility. I have some that looks a lot the same, but the underside is purple on mine. A friend has them with stripes, but hers and mine both are distinguished by the tiny three or four petal white flowers. The stems are more wiry than mouse ear, and the leaves aren't fleshy. Also, mine has longer leaves than mouse ear.
We call this one "baby Jew", the bridal veil is smaller leaf, shinier and darker green with purple under. Bolivian is the one looks like a bee hive, then there is the setcresia that's also called purple Jew and the variegated one (both white and green, and tricolor) there are so many of these~!!
I think this one has pink or bluish flowers.