A brief vision he (Sam) had of swirling cloud, and in the midst of it towers and battlements, tall as hills, founded upon a mighty mountain-throne above immeasurable pits; great courts and dungeons, eyeless prisons sheer as cliffs, and gaping gates of steel and adamant: and then all passed. Towers fell and mountains slid; walls crumbled and melted, crashing down; vast spires of smoke and spouting steams went billowing up, up, until they toppled like an overwhelming wave, and its wild crest curled and came foaming down upon the land. And then at last over the miles between there came a rumble, rising to a deafening crash and roar; the earth shook, the plain heaved and cracked, and Orodruin reeled. Fire belched from its riven summit. The skies burst into thunder seared with lightning. Down like lashing whips fell a torrent of black rain. And into the heart of the storm, with a cry that pierced all other sounds, tearing the clouds asunder, the Nazgûl came, shooting like flaming bolts, as caught in the fiery ruin of hill and sky they crackled, withered, and went out.
So apparently Sauron built the towers - and mountains? - with the ring - "Ring, erect me a tower!" and maintained them with the ring, or rather (because Sauron himself hadn't touched the ring for a long while) the ring maintained them. That would certainly be a useful trick, but (a) you could make towers and orcs and engines without the ring, because Saruman did; and (b) you could get new troops and orcs and engines without the ring, because Sauron didn't seem to need them the second time around. The sensible thing would have been for Sauron and his orcs to put up new barracks and live in them rather than taking the measurable risk of inhabiting ring-built towers, battlements, mountain-thrones, pits, courts, dungeons, prisons , and gaping gates that were liable to sudden collapse.
Other points that come up are Who did he keep in the prisons and dungeons? and What happened to them when the walls fell in?
it's not an entirely trivial point, now I come to think of it; it suggests, surely, that there were disagreements under Sauron, which is to say politics, which is to say that if he was entirely evil (and we never do get to hear his side of the story, do we?) then people who opposed him must have had some good in them, which means that the average platoon of orcs must have included at least one sweetie.