I was recently in Milan and visited some relatives there. At their house, I noticed that they have what I think of as very unconventional downspouts – even though they told me this design is quite common in that area.
In the first photo, you can see the overall downspout. It’s just a set of chains (four, in this case) that run out of the eavestrough down to the ground. In the second photo, you can see what happens at the ground: the chains run into a concrete basin filled with decorative stones. There’s a whole at the bottom of the basin that runs into a dedicated water line that leads to the sewer system (or that can be then reclaimed as grey water for other uses).
Water running out of the hole in the eavestrough remain “attached” (due to surface tension) to the chain, so instead of splashing all over the place, the water runs straight down into the basin.
The advantages of this approach are maintainability and aesthetics. It’s easier to replace the chains than to replace a downspout, and the chains hold a certain aesthetic appeal, regardless of their condition. (We all know how crappy an old, dented, and rusted out downspout can be.)
This is also an example of design by inversion. Instead of constraining the water from the “outside,” as with a regular downspout, the chains go on the “inside” and the water runs on the outside of the shape.