Thank you for the responses - they've been most helpful.
Someone asked for a definition of "prep." To my mind, it is dedicated time spent reading material and/or preparing notes for the upcoming session. A couple of minutes in the shower thinking about tomorrow night's game is not "prep" by this definition. Sitting down at your desk for 30 minutes is prep.
When I posed this question, I could think of three possible ways you might do zero-prep D&D:
1. Pure improv, where you and the players devise scenes keep going.
2. A generative tool that creates the adventure for you as you go. Perilous Wilds is one such tool (it's for Dungeon World, but it is perfectly usable for D&D adventures).
3. A master tome that is concise enough to just consult "on the fly". Some say they used Wilderlands of High Fantasy in this way. The players move to a new hex, the DM looks up the location (at the table during play) and then plays it through.
I think all(?) of the no-preppers who have answered so far have fallen into category 1.