I haven't played a DMPC in years, since AD&D 2e. For one thing, I have enough to do running the wqorld and everyone else in it--usually foes for the PCs. Also, I find it is too tempting for a DM to try to "play too" with DMPCs. I have seen many times that the DMPC in other DM's hands was a tricked-out PC just the way the DM wanted him or her. Players, including me, really resent it when the DMPC dominates the action or the story. I am sure I was guilty of the same things when I played DMPCs, so I just stopped doing it.
I don't like playing in games with DMPCs, either. I've just had a couple of bad expereinces with DMPCs. I like the DM, but he shouldn't be allowed to mix DMing & playing. I would even extend that to NPCs. If an NPC is traveling with the party, they're an ally or a cohort (to use d20 vernacular); and 1 of the players should run that character.
The litmus test I suggest is whether the DM would allow a player to totally run the character (NPC or DMPC or whatever), including giving over a character sheet and allowing the player to make all decisions for the character. If not, it's a "DM's pet" character. Alternatively, if it makes the DM unhappy when the player decides that the character does something that the character "wouldn't do"--it's a "DM's pet"; especially if the DM "over-rules" the player.
I just have little use for this as a DM or as a player.