First, what's wrong with algae? Other than the visual, it won't hurt you. Some cultures actually harvest and eat it. I have ditch next to my house with some algae. It's home to a toad family. I have a couple solutions for you. The best is to fix the ditch pitch so water doesn't collect. If you have a plethora of green stuff, try switching to a lower nitrogen fertilizer. Contrary to what Scott's tells you, these are better for the lawn because it forces the grass to grow deeper roots instead of surface feeding making it more burnout prone in hot weather. Switching fertilizer won't eliminate the problem but it may reduce it.
My first choice is to fix the pitch as I said above. You can also widen the ditch so the water is spread over a larger area which will add in evaporation. Sounds like a lot of work. Just fix the pitch.
If the water is always present, the last natural solution is add a gold fish or two. They will eat the algae.
I know you don't want chemicals, but even an organic thing (like an organic apple) is a chemical, so don't be duped into thinking all chemicals are bad. The least obnoxious chemical solution is Roundup which has been getting bad press recently. Don't get the fast acting stuff. It contains herbicides and other bad stuff. Buy straight old fashioned Roundup. (Only Glyphosate and inert ingredients period.) It will kill anything green in a few days by stopping magnesium process in the plant. Its not a traditional herbicide and is environmentally friendly (breaks down in sunlight, is eaten by bacteria in the ground and is broken down long before it hits the water table. It is almost nontoxic to mammals.) of the chemicals. If you have a local beekeeper they will probably jump on you. I'm a beekeeper and read extensively about Roundup. When properly used, it has its place but that's another blog post! I wouldn't hesitate to use original Roundup. Start slow and be patient it takes many days before you see the effects. Multiple smaller doses is better than one huge concentrated one.