Terminator - To be avoided at all costs (everyone agrees)
Wally - AI does its best to "take care" of us, turning us into infantile, unthinking, pleasure seeking dweebs. The ultimate basal brain utopia. But empty.
Star Trek (TNG) - AI as an assistant to help us fulfill our higher purpose and make us better at being a higher order being. There is no doubt that the ship's computer has advanced AI if you look at the questions posed to it by the engineers and the crew, but it does not impose its "will" upon them. It is an observer until directly asked, even when death is at hand (seemingly).
There is a very good video on YouTube about it, but I can't find it (right now) that explains it in a very accessible way (that's pretty entertaining) with no real knowledge of the underlying functionality necessary. I suggest you watch it. It's great!
As for the Star Trek (TNG) interpretation of AGI, I suspect something like this in the real world would give rise to a kind of "oracle" situation, which creates its own dangerous problems. A system which functions as described only by observing and giving input where asked still has the potential to affect the outcome of events simply by being a reliable predictor.
A paper explaining this concept far better than I would be able to in a HN comment is available here: http://www.aleph.se/papers/oracleAI.pdf
In it, humans are basically treated like pets or toddlers, in that they "do stuff" but they're kind of oblivious to the fact that AI is moving the world forward.
[0] https://en.wikipedia.org/wiki/Person_of_Interest_(TV_series)
In the Star Trek model we see the input directly limited to the data in the ship and surrounding visual areas (as far as i'm aware)
In the Wally model we see that the input is limited to a single optic/auditory/ect location.
We have a potential network that input can come from everywhere cameras, phones connected to the internet of everything. I think it really comes down to with how we want to interact with AI and how much input should it have to directly interface with us.
Also it's very hard to know even during deployment how accurate an AI will have a grasp on human want and interaction. A lot of people are worried about the 'non-consenting' information potentially available to the net. Very few people, if any, will ever really be able to address it should an AI be created and deployed.
It's a very real possibility that solving intelligence would make most of human knowledge work obsolete.
Government and corporations are the ones who will make that call.
Government = Wolf
Corporation = Fox
Average Joe = Sheep
Most of the sheep are protected by a cage; it takes a lot of mental power to operate in the increasingly technical world we've created.
Solve AI and you've removed that cage. Sure we'll still need some sheep but no where near as many as we have right now. Most will be made redundant.
The sheep today that are living fulfilling and happy lives because of their ability to process knowledge marvel at the possibilities of AI and how it could push the species forward but forget to consider what their own role would be in a world where machines are both stronger and infinitely smarter than any human.
Government = The farmer
AI = Plant-based diet
Naively, everyone eating a plant-based diet is great for sheep, but it's hard to imagine a world where the farmer still feeds them.
As technology advances, we run the risk that the strategic calculus changes in favour of one party pre-emptively attacking the others.