I find myself in a situation where my schedule has gotten tight enough that while I can still carve out a couple hours to run a game weekly, I don't really have time to prep. I have run lots of no-prep games, but as one shots or short engagements (3 or 4 sessions, max, usually over a constrained time like a convention weekend). I have never run an ongoing campaign with a zero-prep paradigm, though.
If you have done so, what is your favorite system for an ongoing, no prep RPG campaign? Is the system built for zero-prep? If so, what built in tools make that possible.
First a caveat, I wouldn't say zero-prep, but rather incredibly low prep. But for my money PbtA games fit this style well. Some better than others. Zombie World. Masks: A New Generation. Cartel. I'd say these games are built around the idea of low-prep. PbtA games are designed around the idea of a reactive referee, so you just need to have a little bit of prep done (fronts, etc) and you can get going. Poke the PCs and things snowball from there. It's down to the moves and resolution. The PCs make a move and the situation changes no matter the result. Either they get a success, succeed at cost/negotiate, or they fail. The referee makes a move based on the PCs' cost or failure, further changing the narrative...which evokes more PC moves, which evokes more costs and failures, which evokes more referee moves, etc. Really great PbtA games can snowball from the first move.
If not, what external tools are you using?
Genre knowledge helps a lot with this. If you know the genre really well, you can simply react with some trope that's appropriate and keep things moving. No need to wonder or check the book.
Any general advice for ongoing zero-prep?
Get Return of the Lazy Dungeon Master and read it. It's a great book. It will help a lot. You might not use everything in there, but the ideas are sound enough to transfer to non-D&D games.
Know the genre really well. It helps tremendously.
Do certain genres work better?
Yes, action-adventure genres work better than most others. Horror. Superheroes. Pulp. But anything you're a fan of that you know intimately can work. If you know the tropes of the genre you can put them in the game without a second though making prep easier or unnecessary.
What is a good number of players?
I'd say 3-5. Less than that and you're responsible for more stuff and keeping things going. More than that and it quickly becomes an unwieldy group.
What kind of format (ie episodic versus serial) works best for you?
Either, or. It's a bit harder for me to do episodic as you need to push a satisfying conclusion in one session, so a sprawling serial game is easier to do. Just note where you left off, who's mad at the PCs, what conflicts they're dealing with, etc and pick up there next time.