I currently run for two games: old school D&D (Swords & Wizardry) and Conan 2d20.
For S&W I do a lot of prep: multi-level dungeons, city and town descriptions (sometimes maps), some names of prominent NPCs, brief descriptions of what might be in an overland 5-mile band, some notes concerning what various factions are up to. But chances are you’re still going to be Gaming on the Fly. PCs notoriously do not go into the dungeon (but it’s there, breathing and attentive for whenever the PCs finally want an adventure). They might decide to travel to a town for which you have nothing prepared. They might do absolutely nothing but make plans and have meetings with the local NPCs (my players tend to do this last one a lot. It’s their way of avoiding putting their characters into danger).
My point here is that something is prepared, even if it doesn’t necessarily see use during a particular session. For old school D&D, I disrespect the “Quantum Ogre.” For me, narrative choices matter: there absolutely should be a difference between going down Passage A vs Passage B. Something else to note is that this mode of play is very dependent on player activity. This is why my favored *master term for this mode of play is Referee. The focus of play is on player agency. If an “adventure” isn’t happening, well… “You did all see the broadside advertising for the Tomb of Horrors, right? Well, are you going to go there?”
For Conan 2d20, in contrast, I tend to select a pre-1950s Weird Tale for inspiration, use that for the story situation, stat out some NPCs, then throw the PCs into it. That kind of game is also reliant on PC activity, but my GMing is much more reactive to emerging narrative. Most notably, I don’t bother mapping what I may presume are going to be key locations. Conan 2d20 is almost a super-crunchy Story Game. “Dungeons” can organically assume the proportions of narrative need, not simulationist exploration. In short, the Quantum Ogre is welcome here (in exchange for my GM resource of Doom).
Now, were I to run S&W “on the fly,” with absolutely no prep… That’s why I have a binder of old standards, some mini-dungeons. I’m late to the old school scene, so my standards aren’t the usual suspects, I’m sure. Three are Creation’s Edge’s “The Cursed Fountain,” Jeffrey Talanian’s “Rats in the Walls,” and Matt Finch’s “Tomb of the Iron God.”
For Conan 2d20 I’d rely on memory. A really good scenario has been based on Clark Ashton Smith’s “The Charnel God.” But I can see spontaneously creating from whole cloth. Conan characters are built bristling with plot hooks. It would be easy enough to look over the characters, drop them into something, then observe what happens.
I expect different games require different degrees of “preparedness.” For my two favorites, whether maps are important or not seems to be the chief consideration. I expect it would be fun sometime, as an experiment, to burble something out of an online random dungeon generator and just run it!