Ivy would be on the bad list as it's poisonous. here's a blurbette on english ivy;
"English ivy (Hedera helix) is an indoor and outdoor ornamental vine. This plant contains saponins, which have caused poisoning in cattle, dogs, sheep, and humans. Two chemicals in the sap can also cause severe contact dermatitis in sensitive humans. Cases of poisoning are found in older European literature; the plant grows naturally in Europe. Cattle that ingested large quantities of the vines were ill for a few days. Humans who ingested the berries have shown symptoms, including coma. Dermatitis is rare but can be severe. Weeping lesions and blisters respond slowly to treatment (Cooper and Johnson 1984, Massmanian et al. 1980). Family pets should not be allowed to eat English ivy leaves."
You have a couple of alternatives. one is to get a plastic ivy plant or two. There's one brand that's widely available at pet stores that several people on here use. I'll see if I can find a photo.
Alternatively, you can use any of a variety of aquatic plants. I think several are mentioned in the link emmanelson96 provided. The general rule is that any plant that's safe for fish will also be safe for turtles, but some plants are harder to grow. Also, since the turtle will probably rip it to pieces, you probably don't want anything expensive.
(edit0
here's a thread with photos of a very effective use of plastic plants. on page 10 of the thread (it's a long one) there's a photo of the package that the plastic ivy comes in;
http://www.redearslider.com/forum/viewt ... sc&start=0
My turtle's very favorite green thing is fresh basil. He's loved it since day one. I grow it so there's always some around. I've read about other turtles on here that love it too. I would not feed a turtle herbs that are strong like rosemary or mint. Some of the others like sage and thyme would probably be good. I've read about turtles that are fond of cilantro. Parsley is on the bad list because of one of the substances found in it.
