In the Champions game (and related games using the Hero System), a character may have a DNPC, or "dependent non-player character". This is a character controlled by the GM, but for which the player character is responsible in some way, and who may be put in harm's way by the PC's choices. (Spiderman's Aunt May is a good example of a DNPC.)
There is some discussion as to just how important fully fleshed-out NPCs are in any given RPG, but it's general consensus that the more "real" a NPC feels, the more fun players will have interacting with him in-character. Gamemasters should remember that just like a player character has hopes, dreams, and goals, so does every NPC, and player characters getting in the way of them could lead to unfortunate encounters.
There is also debate about how much work a gamemaster should put into a NPC regarding game statistics - some people prefer to have every NPC completely defined, with stats, skills, and gear, while others define only what's necessary and fill in the blanks as they go along. This is often the approach with gamemasters who GM "on the fly".
The term is also used in some types of video game to describe entities not under the direct control of players.