I've had or run into just about them all;
EgoPCs: these are the DM's former characters from past games. They can't be beat, only worked with or for.
(in an SR game, the GM had such. They were horrible. I took a shot at one, he told me I missed. I pointed out I hadn't rolled yet, so he said roll. I rolled, he goes "you miss" and I dropped out of the game later on, when it got WORSE.)
DMPCs: when the group is short handed, or there's a spot ("we need a rogue") that no one wants to play, or, in my case the players never let you play, you're always the DM. I've had these and they tended to be low key. My DMPC's didn't instigate stuff, and were basically extra healing and strength of arms. The players really did seem to enjoy it, regarding it as another player.
PlotNPCs: these are those NPCs that you stumble on, and they stay with the group, even though you don't need them, and usually don't WANT them. They are some future plothook, so you're supposed to work with them, even though it's horrible metagaming, since you don't like them.

(a game I'm in had several of these at one time, they were too irritating in speech and manner, and too often instigated things where the rest of us didn't want to get involved.)
The main problems I have is when they overshadow the PCs, but you also have the matter of more dicerolling. Once my brother was DMing, and it was combat. In a game we weren't familiar with, it was running slow, but then we reached a part where a bunch of NPCs were fighting. We performed our actions, and it took him nearly a half hour to go through all his NPC's actions.
The problem with the egoPCs is broader than liking your NPCs, the DM even stated in a later conversation that "the story is mine, the players are just watching it unfold". Huge difference in gaming style from what I prefer, and even without that, I'd never play with that person again.