While passive, neutral, and hostile may seem all-encompassing, there are some unique mobs in Minecraft that do not fit within any of these descriptors. For example, the players themselves are technically mobs. This can be much more prudent in multiplayer servers, but even in single-player worlds, you will still be controlling a mob.
There are also some mobs that were cut from consideration like the killer bunny or the mythical Herobrine. While you could argue that the killer bunny was meant to be a hostile mob, it falls in a unique category of unreleased mobs in Minecraft.
To read more about these mythical creatures that almost premiered in Minecraft, there is a collection of articles below.