I'll use the definition of "a character who is near--permanently attached to the party and run by the GM" as my definition of a GMPC. "NPC accomplice" might be a better term, implying the subordinate role such a character fills in my games.
I use them, when the group is small, or missing vital roles. Or, when it fits the story being told. However, they are near-universally weaker than the PCs (gen them as lower-level in DnD, less BP/Karma in Shadowrun, etc) and typically fairly passive.
They've also proven useful as a way to offer up reminders or plot information when the team gets stuck or forgets something important, though not to put them back on a pre-determined plot line. Think "Oh, hey, didn't we hear from that shaman a ways back that there's a powerful toxic spirit living in here? I don't know that we should just barge in..." as opposed to "Hey, we're supposed to be breaking into the bank vault for Mr. Johnson, not researching his sordid past & deciding to stick it to his mega-corp ass!"
That being said, as a full-time GM, there's enough on my plate, as others have previously said, I try to limit the use of such characters. More over, I try to use ones already viewed as fallible / inferior (to the party) NPCs to discourage any unconscious desire to be the center of attention. I'm already the whole universe, minus the stars of the show, so there's little need to stoke my ego. But, I'm metahuman, too, I wouldn't be surprised if I've tried to turn an "NPC accomplice" into the star of the show. Fortunately, I have a good group of runners who'll swat me upside the head, then kill the guy in his sleep to make it stop. And laugh at me mockingly if I try to railroad them.
If you guys are reading this, I kid, I kid. Maybe.
All the bad things people have said about GMPCs are valid & true. But, sometimes, that long-running NPC accomplice can help bring the world to life and gives the GM a way to pass along in-world advice and reminders to help keep the story rolling. If you're group is comfortable enough with you as a GM, and understand that when you speak as the party's NPC accomplice, you speak with his limited knowledge and capabilities, an NPC accomplice can be a great addition to the group.
The true GMPCs, where the GM expects to be a "star" of the show, control the story, rather than direct it, and handle the encounters, drown the group in a sense of pointlessness. The game goes on, with or without them.