I believe the stuff sold as 'lucky bamboo' is a variety of Dracaena, and I imagine it would do pretty well in a riparium.
Pothos is pretty much a classic, and I've had some sort of ivy before.
As to grass-like, the closest would probably be some sort of reed-like marsh plant. check some of the local pond shops or greenhouses. Sometimes even a home center will have a small section of pond/aquatic/marsh plants.
I think hydroton is used because it's been used with hydroponics (which isn't really that much different from a riparium setup), is relatively cheap, and pretty lightweight.
If you had nothing else, you could probably even use just straight gravel, but something like small lava rock or pumice might be better.