Feeder machines?
A large and horribly deformed member of their own species?
Another kind of animal?
I realize to ask what is going through an animals head is pretty pointless.
But this question has kind of bugged me for a while.
I watched a documentary that said it was the second on your list.
And more recently I watched a documentary that said it was the first and 3rd - (that cats, for example, have evolved ways of taking advantage of humans in order to be fed and looked after - take meowing - it’s supposed to imitate the sounds of a human child or baby - causing the human to want to respond with care of food)
my last ‘of’ is supposed to be an ‘or’
Dogs see you as “family.”
Cats see you as “the help.” 
Given that dogs are pack animals, I’d speculate they veiw their human family through the lens of pack heirarchy to an extent.
Also, there have been studies that note that adult domestic dogs evidence the same sorts of behaviors as adolescent wild canids, leading researchers to believe that domesication has left dogs in a state of eternal youth, from a psycological standpoint.
So to a dog, we’re sort of older pack-siblings who have enough experience to go out on hunts and bring food back to the den for them.
As for cats? I think they see us as “thumbed slaves good for operating the can opener and giving attention on demand.” 
Essentially, to pack animals (dogs) you are a member of the pack. Which is why it always bugs me to see people treating a dog like a human. So many people have trouble with dogs because they forget that it’s a dog and that the dog thinks it is living in a strict hierarchical society and behaves that way.
I have no idea how cats see humans, but I don’t imagine it’s very pleasant.
Dog: “These people feed me! They must be gods!”
Cat: “These people feed me. They must think I’m a god.”
My dog sees my roommates as telepathic door openers. Unfortunately, none of are telepathic. He treats me as the Alpha dog, leader of the pack. And yes, at almost 4 years of age he still exhibits puppy behavior (licking, play bows) to almost all people he knows. This leads me to believe that he sees all adult humans as above him in some kind of dog-pack hierarchy. As for children, I haven’t seen him around enough to make any more judgements except that he is even more playful.
Cow: “Mmmmm. Food.”
Chicken: <white noise>
“domestic animals” includes livestock as well as pets, though the thought processes of many of those species are probably best described as minimal to nonexistent, at least we hope they are, in many cases. Otherwise, Orwell’s classic “Animal Farm” is more of a treatise than an allegory.
Still, pigs are perhaps the most intelligent of domesticated animals - how do they see the pig farmer?
Ditto on the dogs see you as an alpha member of the pack. I’ve heard cats can see you as a mother surrogate in some ways, which explains some behavior like kneading of the paws on you while you pet them. Kittens do this to their mothers when they nurse.
Flower In a Pot: Oh no not again!
sorry, I couldnt help myself.
Apparently, after being domesticated for 30,000 years, dogs have evolved so that they can read human expressions and understand what their master is trying to communicate to them. This can even be seen in young puppies suggesting that they have evolved to such a state where they can understand some human gestures from birth.
It also depends on how you treat them and train them.
Cats that live in groups (like prides of lions) do have a heirarchal system. The rule at our house has always been: “Never feed the cats first thing.” If the first thing you do when you come home is feed the cats, and the first thing you do when you get up is feed the cat – the cat thinks “As soon as they see me, they feed me. I am boss cat! They serve me.”
So if you establish yourself as “boss cat” you are just a weird, tall two-legged cat, at the top of the food chain.
They also behave better when they think you are “boss cat” because your commands actually mean something. If you’re “boss cat” and your cat hops up on the table, when you say “No! Bad cat!” the cat will jump of the table right away. If you’ve let the cat think it’s the boss, when you yell “No! Off the table!” the cat will look at you as if to say “So what are you gonna do about it?”
Cite?
Cite?
I’ll back up MC Master of Ceremonies to the extent that I heard a report on NPR about a study on dog intelligence that more or less found what he asserts. Dogs, even puppies, were better than chimpanzees at interpreting human gestures. The authors posited it was a natural selection thing; dogs that figured out what we wanted (and maybe more imprtantly, didn’t want) were more likely to contribute to the gene pool. I’ll try to google around to see if I can find the article.
I read about that too, but I also read that there would be similar evidences concerning humans as compared to other primates. We would retain juvenile traits too.
Dogs Best Friend (NY Times)
About ten years ago, I saw a movie (can’t remember which one) which took a dog’s point of view. The dog referred to people as “the ones who can make stones fly”. Maybe that’s how they see us.