When Planescape first came out, dungeon crawling was probably at its absolute nadir of popularity: this was the mid 90s, when the World of Darkness was in vogue and everything had to be edgy, story-driven (i.e., largely railroaded) and infused with angst, drama and meaning. So the idea that you could use it for old school dungeoneering was never made explicit in the published materials; I think the designers wanted the players to do more "mature" things with the setting, whatever that meant.
But dungeoneering is certainly implied in the Planescape if you look for it. Planes like Pandemonium and Baator basically are big dungeons, and Sigil is the start location for an old school-type D&D campaign par excellence - a place where you can buy and sell anything, go anywhere (if you know the right people and can find the right portal keys) and get involved in politicking and advancement. The pattern, I suppose, for this sort of campaign would be:
- Start in Sigil. Use it as a base for dungeoneering exploits throughout the multiverse.
- Make lots of money, gain levels.
- Get involved in politics and advancement, reach higher echelons of a faction if that's your thing, start branching out into the belief-oriented specifics of the setting.
- Create your own realm somewhere, except you can do it anywhere in the multiverse if that's what you fancy.
The ultimate Planebox megadungeon is, of course, The Abyss. The Abyss is the Chaotic Evil plane, ruled by the Tanar'ri (okay, okay... "demons"), but absolutely infinite in scope: there are countless layers of The Abyss, each of which is infinite in its own way. There is literally no constraint on the imagination of the DM in coming up with whatever the hell he wants within this plane; it can be as fantastical or mundane as he desires, and there is no requirement whatsoever for any of it to make sense - listen, this place is infinite. Do you want an entire dungeon that is really a forest, but the branches of the trees are all actually snakes? Do you want a dungeon that is actually the digestive tract of a gargantuan whale swimming in an infinitely large ocean? Do you want a dungeon that is made out of mirrors and populated by glass golems? It's all there and more. Best of all, for the adventurer, anything that you could possible desire is in there somewhere: the only problem being that you have to negotiate an infinite amount of Chaotic Evil entities and an infinite amount of hostile environments to get it.