The Mythic Game Master Emulator is pretty good for solitaire play; it’s actually more ambitious than just random dungeon stuff, it’s meant to allow you to use charts to randomly determine much more open-ended adventures. There’s a demo pdf that lacks the main chart, so you can’t actually take it for a test drive, but it does give enough explanation (I think) to get a sense of how it all fits together. Basically it gives a structure for asking yes/no questions and resolving whether it’s a strong no, no, yes, strong yes depending on the odds and how “chaotic” the scenario has become and whether a random event has occurred and if so what sort and whether it interrupts the logical flow of the scenario. A random event isn’t just a wandering monster but something like: Move toward a plot thread, Action: Expose, Subject: Jealousy, and then the player has to interpret what that means in the context of the adventure so far. If nothing suggests itself, it’s just dropped.
It’s surprisingly easy and satisfying, particularly for strongly structured stories like exploring a dungeon (possibly supplemented with random monster and treasure charts for determining things like what precisely is lurking in the cavern that the Orcs won’t enter) or perhaps a manor-house murder mystery…it takes a bit more practice and comfort with taking a “director stance” approach to at least some of the play for a really open-ended story, but it’s really good at keeping you from knowing everything that’s going to happen in advance on the one hand and having the adventure feel completely random and undirected on the other. Even though once you grasp the system, it really boils down to about 2 pages of charts (out of 54 pages), besides explaining the system the remaining pages do have a lot of helpful examples and advice about how to use it and how not to “cheat”… I found it well worth the $7.
I haven’t yet tried to use it for play with other players, and I’m not sure I will…though I can imagine keeping the chart around as a source of inspiration if the players hare off in a direction I wasn’t expecting and nothing immediate comes to mind.