I wanted to share a project that my son made for me. It is called a Rain Chain and this is how it works. When it rains, the water runs off the roof and down the chain into the "catch basin". (In this case we used a terracotta pot with river rocks in the bottom.) The pot helps the soil from eroding and the water goes into my lily bed. It was pretty simple to make and I think this looks a lot better then a traditional plastic or metal downspout in this spot on our sun room.
Here are instructions on how to make your own Rain Chain.