I have RolePlayed without a GMPC (Game Master controlled Player Character) exactly once! The players harassed the character I'd designated to be their contact to the underground for no reason, they shot an old man to death, and burnt down a building (That last one was by accident, but still...). Then they spent the next couple of days roleplaying the downtime they had in between missions, which I had no involvement in what so ever. The next in game morning, I introduced my GMPC, who had her own sub-plot that was never fulfilled by the campaign's end unfortunately. After that the game was our second most successful RP amongst our group.

Now that I think about it, the best GMPCs that have been involved in our group were characters who were some-how incorporated into the campaign's storyline.

I don't have much experience with RolePlaying with people who aren't close friends who I didn't meet outside of setting up the RP, so things like God-Modding, misbehaving players, DMs being an asshole and Munchins aren't really things I've ever had to deal with.

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One of the biggest obstacles I've encountered as a DM is actually getting the players to let me actually DM. One RP we did, somebody wanted to play as a Chaotic Good [url=http://img4.wikia.nocookie.net/__cb20120622225324/mlp/images/5/5b/Changeling_swarm_S2E26.png]Changeling.[/url] I rejected the idea out of hand (Both because Changelings are arrested on sight, ESPECIALLY if they try to disguise as another race, in this particular setting and because we already had another special snowflake in the form of a Chrystal Pony, who I'd already established beforehand didn't exist in this setting but the player really wanted to play a Chrystal Pony (And their character ended up sucking so hard that they single-handedly ruined the RP anyway!)) and they cracked the shits at me.