I say DMPC, because D&D is what I play, but really, it could be GMPC as well. I tread fragile ground.
Anyway, I noticed I was getting pretty bad with the Inevitable (my DMPC in Black Earth), so I made myself up some rules to follow. A visual thing so I don't forget you know? Originally they were going to be geared more specifically to that character, but then I realized it would be better if they weren't, and maybe other people could take some wisdom from this.
I was hesitant to have a DMPC at all (i've never done it before), but my PCs party constantly argues and can take upwards of two hours to decide a course of action. Seriously, they once spent an hour buying breakfast... from a bread shop.
Edit Thank you, everyone, for your wonderful advice - really, great suggestions for me to try and adapt to my style of DMing.
I had hoped the resulting discussion would have been more about GMPCs in general than about how to handle slow PCs. I love my players, I really do. I'm a very lucky DM to have a group of people that work so well together (even if that work is slow).
I also feel inclined to give a bit more description as to why I included a DMPC in my game, since it seems like some people are under the impression it was just to moderate the PC party.
He's a tool to introduce more adventures - a time-traveler (this was the original concept). I'll admit I pretty much stole the idea from Doctor Who - but I wanted to be able to jump my players around settings and get them to the action.
I really want to play. I... never get to be a player. I've never been a player in a game that lasted more than 2-3 sessions. Having this character lets me have a way to interact with the game from the other side as well. I've got NPCs, sure, but they're not really... the same... They don't stick around long, they don't follow the same rules... /Edit
I'll write up rules for him specifically later (being a time-traveler he really
needs them, lest I get confused and contradict myself every other session). Also, his personality has gotten a bit wonky - which is really saying something since he's completely mad. (He's a generally cheerful fellow, but the PCs are just.... so obnoxious.)