I have two rabbits and a cat, and we like to say around the house that the rabbits have no theory of mind. That is to say that they treat everything like an inanimate object. It's clear that they don't attribute any thoughts, feelings, or motivations to the cat or myself. This can get them in trouble when the cat doesn't want to be bothered.
In humans, we start to develop a theory of mind at around 1 year of age, around the same time as we begin to acquire language (see http://amzn.to/thM6Rz for more), and it's usually fully developed around 3 or 4. There are canonical experiments to test this (http://bit.ly/sccmfN), but a baby's changing reactions to the game of peek-a-boo is more than enough evidence for me.
I've begun to notice that though it's said to be fully developed, one's theory of mind never really gets very robust. The phenomenon is exploited often in film and theatre, when, for example, an actor looks up at a sign. Even if the sign is in front of the actor, so in reality the actor is looking at the back of the sign where nothing is written, the audience will assume that the character is reading the sign. It's called "cheating the eyeline."
Plots are cheated just as much with a similar technique. You may have heard movie fan boys complain of plot holes like, "how could Sarah have known that Ben was her father if she never met him or Susan before that night?" Well the truth is she couldn't have, but most people don't notice because they assume that all the characters have the same information they have about the plot.
When that's not the case, the filmmaker or production company has to make it very clear, otherwise the audience will get confused about who knows what. That explicit indication of differing states of knowledge between the audience and the character is called "dramatic irony." Don't ask me why.
What does this have to do with game design? Firstly, it relates to enemies and other NPCs, and secondly it highlights a slightly disused mode of gameplay.
NPCs depend on being attributed a mind by the player. Whenever you break those principles (for example, http://bit.ly/tyg8IC), a game can become very frustrating very fast. On the other hand the player wants to believe, and good game designers know how to exploit that. "The Sims Social" uses "cheating the eyeline" quite often. When my Sim needs to use the bathroom in someone else's house, he goes to the bathroom. There's no question as to how he found it.
It's also worth thinking about the mind of your playable character. Most of the time games have an avatar; a mere stand-in -- a placeholder for your consciousness within the game world. In these cases, dramatic irony doesn't make sense. You are the character, so how could you have different states of knowledge?
However, there are a few cases when the player is none of the characters on the screen, and now you can start to have some fun with the theory of mind. For instance in "Black and White" -- being frustrated with your Creature is an important part of the game and ultimately, in my humble opinion, makes it more fun.
The same is true of many an RTS. Why are your AI fighters attacking the wrong thing? Well, in some cases it's because they don't know everything you know about the playing field, and that makes them all the more real.
In summation, I think it's fair to say that imbuing your characters (playable or not) with a sense of mindfulness, with thoughts and intentions, is a difficult balance. Players will give you the benefit of the doubt, but that benefit only extends so far and for so long.
So when the guards in your game hear a sound, have them look at where the sound is coming from. Let your soldiers have a moment of awe when the dragon attacks. Give your scientists a reason to be walking around. Are they looking for something? Are they going for lunch?
Your players' theory of mind is worth getting right.