In addition to the general use of Roman-type plumbing I briefly
alluded to, consider the placing of some Middle-earth cities on
geographical features conducive to moving effluvia. Minas Tirith
and Minas Morgol on the lower sides of mountains, with gravity
assisted streams to carry materials to nearby Anduin and the ocean.
Even Edoras has a middling stream going through the town/citadel
to the Anduin. Ditto Lorien (and anyway, you'd think giant trees
would be in need of many nutrients---of course, how elves living
near treetops (like Galadriel and hubby disposed of stuff, well, it
does bring them "down to earth" a bit, as it were).
Which brings up the issue of Gondolin. They had to have a pretty sophisticated
system to dispose of materiel out of the plain and towards Sirion, SO
WHY DIDN'T THEY USE IT TO ESCAPE. Come on, couldn't have been
that much worse then going through a London Sewer.
Oh, and the green leaf above is an air freshener.