How the AI behaves and reacts to the player and the game world as a whole can have a huge impact on many things throughout the players time spent playing, from immersion to gameplay and things beyond.
Having bad AI and things can quickly pull the player out of the game experience when something goes wrong or feels unlogical and out of place within the game world.
I: AI Gampelay.
When it comes to direct-gameplay AI one of the most important aspects is how that NPC reacts to the actions around it. What the AI can do in situations impacted by both the player and other NPC's. Some games, such as stealth based games (IE Thief/Splinter cell/Metal gear solid) put a high importance on the AI in terms of line of sight and sound. What the AI sees in the world, if shadows impact it, and what it "hears." However this kind of AI is typically scaled back for non-stealth games. The AI might have a cone of awareness around it (IE mmo's AI usually) where you simply get close enough, even from behind or such and it knows exactly where you are. Other times the AI won't know of shadows and what it should see/shouldn't see.
To me, a good AI is AI which acts and behaves logically to it's surroundings. One where it has an actual line of sight but not super-human abilities. Things such as foilage and shadows have a meaningful impact and players can make use of them. Things such as sounds play a role as well .
When it comes to having AI like this it is also an important thing not to restrict the players. Let them have fun with the AI in logical and meaningful ways. For example:
1. As sounds play a role, different clothing should affect this. So for example la full suit of plate armour would be a lot louder and noticeable to the AI whereas wearing simple clothing or something would not be.
2. The things within the environment need to be able to be affected by the players. Things such as putting out lights with a weapon. Using a rock and then throwing it to distract a guard, etc. These things can greatly affect how a player can choose to play the game.
3. Disguises. Being able to dress up as a guard, a bandit, or some other means SHOULD affect the AI. If you have a quest or reason to get someplace and you have the means to "acquire" clothing/armour which those tpyes of people wear then it should affect how the AI sees you.
II: Reputation:
Another more impact from the AI to the game world is how the AI reacts to other things within the game world, usually the reputation of the player to them. Things such as when the player commits crimes, murders an npc, etc. This is a MAJOR feature of the AI in an open world game populated by hundreds/thousands of NPC characters. If you steal something and no one sees it, it should not be magically "known" to an AI, there should be no magical "good/bad" to stealing, you either steal something and get caught or no one is the wiser. However if you DO get caught stealing it shouldn't be a huge widely spread thing. IT should start out small. You steal from someone and they catch you, then they know about it. If you steal from someone in a city, then they tell the guards (but actually TELL them, not simply "oh I see you, know the guards all rush in and magically knew you were in here stealing!"). Once you get caught int aht way then your thievery is spread within that town/ivllage/city, but not the entire-world.
The same thing goes for murder. If you kill someone and no one sees you, no one knows it was you. However if you are seen that person alone knows you. However if you are seen by many/guards then you are "Flagged" within that city (if you aren't caught) which then they'll put up posters for you and such and the city is on the alert for you. If you keep up either, murdering/thievery and get caught a lot, it becomes more and more widespread and you build up a reputation to various people within that limit.
However doing such actions should NOT affect all the NPC's in the same way. This is another key thing, with open world games you n eed AI's that are extremely varied. Not everyone is good, not everyone is bad, and most of all, good/evil is all in the eye of the beholder. So what you do within the game world should mean and affect different things to different npc's in that world. Some people certainly wouldn't like that you steal, while others, like other thieves/scoundrels might look up to you actually. Same goes for murdering or doing other things. You might even become so well known for your actions that people start to fear you and react to you in such a way. They DON'T like you, but at the same time know you are a cold blooded murderer so they even give you discounts out of sheer fear of you. This all applies to the other end of the spoon as wlel, for people who are good certain people would obviously think of you differently. Guards might be more helpful in certain situations, friendly lnpc's would give you discounts, howeve rthe more seedier people would look down on you and if you become too well known for being a Mr. Goody two shoes you might even find out that say, the head of the thieves guild put a price on your head to get rid of you.
Reputation in ithe game world should not be balanced on any kind of "good/bad" scale as it's done in some other rpgs (A la fable, kotor, etc). Rather it is simply your reputation that THAT specific AI knows about and how they react to you, nothign more aond nothing less. no magically behind the scenes game trickery that feels "artifical" and unlogical. The players reputation in the world should feel like it has an impact, but it needs to feel logical, not artifical.
III: Wildlife AI.
Wildlife (which refers to the non-human animals and creatures out in the world) can have a huge impact on the players immersion in the world as a whole as well. While humanoid npc's play an important part int he game world, so do the other animals and creatures that populate the world over. It's a shame that many games just treat them as window dressing, a simple "spawn" point here and they just stand about waiting for the player to find them and either kill them or ignore them. This kind of AI feels very bland and gives no "life" to the world. The animals are generally given less AI to work with and feel like cannon fodder to lv up with.
The wildlife AI should be treated with the same importance and care as humanoid npc AI. However it has to be it's own, they aren't humans after all. Animals should not simply stand around, waiting for something to happen. The animals in teh game world should behave like you would expect. Some animals should be passive (IE deer, etc) while others would be aggressive. Some would be territorial, only defending their territory. some might be herd animals which travel in large groups whereas some are pack animals, sticking with a group while others are loners or just stick with their own family.
The next main thing is very important to wildlife. They NEED to have a need to eat/drink. This is something animals do, it's a driving force behind basic instinct in wildlife, the need to find food and water to life. however in most games it's often ignored, this is where you get animals that just "stand about" because they just were given no thought of what to do or behave.
The animals have a simple hunger system where they hunt and find their food (Obviously certain animals eat meat, others eat plants, whereas some eat both). This leads to the wildlife AI coming to life. You have them not only behaving in a variety of ways depending on what type of animal they are (IE pack/alone, plant/meat eater) but also interacting with and against other wildlife.
A few games have started to do this kind of AI with their wildlife, and it really helps make the world feel more alive. It was done a long time ago in Gothic and more recently in games such as Red Dead Redemption (God I hate cougars).
Sorry this is a bit of a long post I just wanted to present my thoughts and things on AI and hopefully we get some of the more advanced AI and things in TES V.