At my current house I have flexible downspout adapters
attached to black corrugated pipe that runs underground out to pop-up emitters in the yard. This is a relatively easy and inexpensive way to manage the water and I haven't had any significant issues. I've mulched a few of the green pop-up caps when scalping, and I used to have a few leaf clogs at the caps until I switched from the NDS pop-up caps to the StormDrain Clog Free hinged caps
. Otherwise this setup has worked fine. They have been in the ground almost 10 years. I don't have any more than two downspouts connected to each pop-up emitter, and most of my runs are pretty short (6-20 feet).
All that said, I think the proper way to do it is to use catch basins, so at my new house I am installing NDS catch basins
under each downspout and using PVC sewer/drain pipe instead of the black corrugated pipe. I have purchased NDS pop-ups
from my local supply house, but only because I am installing catch basin filters
in each box. If I was piping direct and/or not using filters I would definitely order the hinged caps I linked above. Also, instead of using the flat grates that come on a standard catch basin kit, I am purchasing the components separately and using the NDS Downspout Defender
grates. They seem like a more robust design that is less likely to get covered up with mulch or debris. Atrium grates
are another alternative.
All of that comes at a significant cost though. The setup I have where I live now was inexpensive - like $5 for a flexible downspout adapter, about $0.88/ft for the black corrugated pipe, and $20 for a pop-up emitter. At the new house I will probably have close to $100 in each of the catch basin setups, $1.38/ft in the in the 4" sewer pipe, and the same $20 in each pop-up emitter.
Here is a video that demonstrates using a pressure washer to install a PVC drain pipe under a sidewalk. He makes it look relatively easy, but I would probably run into a rock or something.