So there's this paved drainage ditch next to my house. It's a long story, but basically there is water continually flowing into it very slowly from a source I cannot control. The water is rather shallow, and is growing algae.

Is there something I can plant in this ditch that might take hold? I thought about water hyacinth, which I could then compost, but I think that might lead to trouble somewhere down the line after a flash flood if it gets into the drainage wastewater system. Thoughts?

Water Hyacinth is an illegal plant in Texas. There are many lakes in Texas that have been taken over by invasive plants and the control is almost impossible. Please look at this web site and consider going to a meeting to ask questions. This group, the north texas water garden society, is very friendly and helpful.
Tony M
http://www.ntwgs.org/articles/illegalAquatics.html

Howsabout pothos?

If height is not a problem, consider planting horsetail reed, a prehistoric plant that Howard lists in a few of his books. It has to have constant moisture and is a unique looking plant. Gets really tall, though, 8-10 ft I think.