Is there such a thing as a Native Water Plant that isn't invasive and is not String Algae?

I grow Golden Club (Orontium aquaticum), Pickerel Weed, Sagitarria latifolium, Parrot Feather, Equisetum (Horsetails),Water Cannas,Water Iris, Acorus calamus (Varigated Sweetflag), Zephyr Lillies in two colors (White and Yellow), and a couple of water lillies.

Pickerel Weed, Equisetum, Parrot Feather, Acorus and Water Lillies can all get a bit unruley, but pull up easily.
Check out pond plants from Bonnies Plants at Bonniesplants.com or http://www.bonniesplants.com/PondPlants.html?gclid=CJ-xzYmL2owCFR6AWAodAR7bKQ or check out all the available plants at the web site I have listed below.

Here is a link that might be useful: water garden plants

In addition to several of the plants mentioned by vroomp, I have Green Arrow Arum (Peltandra), Iris prismantica (Slender Blue Flag), and a couple of the "invasive" introduced plants, Pale Yellow Iris, Iris pseudacorus, and a floating Fern, Salvinia minima, which, if not contained, will cover your entire pond in a fortnight!
I am also growing a couple of Shrubs/small trees in shallow water, Viburnum cassinoides (Georgia Raisin) and Snowbell(Styrax americanus).
Once had a yellow Butterfly Ginger Lily(Hedychium sp.) in the pond, but when in bloom, it was THE Jap. Beetle magnet of the neighborhood. After a few years, I became tired of fighting the pests and trashed the plants.

I don't have a pond so I don't have any experience with native pond plants. Although after reading the article about ponds in a Buckhead landscape in today's AJC Living section .... it's a tempting concept!

You might want to post a message on the GNPS message board. I think more people read it than post on it, so someone might be able to offer you some ideas.

This link has some interesting points and a resource page.

Here is a link that might be useful: One article about it (sort of)