As reported in a Rec Listed diary today, India apparently just created an unprecedented new category of legal entity with little fanfare - the "non-human person" - in banning the practice of holding dolphins in captivity. As limited as the scope of the specific policy is, and the low probability of enforcement in a country like India, the fact that a national government somewhere declared dolphins to be persons is a BFD.
Dolphins are the most obvious candidate for non-human personhood, as today we know that they (a)have a language, (b)have individual names, and (c)are known to rescue humans even in the wild with no training. The fact that they seem to like us certainly doesn't hurt, and the feeling is pretty mutual. That's obviously not a prerequisite to recognition of a creature's inherent personhood, but it definitely makes dolphins the most likely to be first in achieving that recognition.
Also, they're just different enough from us that we don't have the same contempt we have for other primates: To call another human a monkey or an ape is an insult, but nobody uses dolphin as an insult. If one were to draw an analogy between another human and a dolphin, it would most likely be a compliment of their agility, gracefulness, and other good qualities. Ironically, it's the very similarity of Great Apes to humans that has kept us from respecting them, because to some extent we already think of them as idiotic, corrupted humans rather than creatures in their own right.
So some reevaluation of attitudes might be needed before apes get recognition, but everybody loves dolphins - they look cool, they're graceful, their mouth anatomy makes them look like they're constantly smiling, they symbolize fun and benevolence, and human cultural lore is full of stories of their helpfulness. Of course, once we can actually communicate with them on a complex level, that romanticism will probably be shattered as we realize that some non-human persons are assholes. I wouldn't be surprised if they have racial epithets for other cetaceans.
On the other hand, because their environment is fluid, their thoughts probably are as well, and learning to thoroughly communicate will probably be even more difficult than we think because of that. Human languages all have rigid concepts because we deal with manipulating solid objects, but to a dolphin the solid ground is the Danger Zone where they could end up beached while the flow of water is Home. We know they have personal names, but how they deal with things like nouns could be quite exotic if their thinking is more fluid than ours. We know they can understand specific objects and verb-object relationships, but we still know very little about how these concepts are treated in their own language.
Also, because dolphins are so socially fluid and live in tribal societies, there could be a massive diversity of dialects, and possibly even multiple separate languages. There's also the fact that there are multiple species of dolphins among the world population of about 170 million, and the apparently smartest - bottlenose dolphins - are only one of them. It's not really clear what kind of relationships these various types of dolphins have with each other: Are bottlenose dolphins to other types what we are to apes, or is it more subtle than that? Do they all have language? How do their languages differ?
There are all sorts of fascinating possible consequences to declaring dolphins to be non-human persons, especially once we can communicate with them proficiently. Maybe there are things we could make for them that they'd like, and in return they could serve as lifeguards and sea rescue patrols, do our fishing for us, voluntarily carry scientific equipment to study other sea life in the wild, and other tasks. The US Navy already trains them for mine detection, which is a bit ethically dubious since we can't communicate to them the risks they might be taking, but once we can communicate they might still be interested in return for something. With some specialized tools, they might also be able to do underwater construction. Or not. We don't really know them yet.
It's a bit comical to imagine, but maybe someday when we can talk to them they'll have specialized transportation devices where flipping their tails as they would underwater powers a wheeled apparatus that lets them move around on land while their skin is kept wet. That would probably be uncomfortable, but some of them might be curious enough to want to explore the land. They are curious people, to all accounts.
Other animals are a more difficult proposition. Apes, as mentioned, are perceived culturally among humans as mockeries of us rather than beings in their own right, and it doesn't appear that they're as intelligent as dolphins or that they have their own languages - although they can learn very limited sign language. If they are designated as non-human persons, there's not much chance that they would be able to be granted sovereignty over their own affairs, since communication on a complex and abstract level does not appear likely. Still, they would have the right to be left alone and not be caged.
The weirdest future candidate for personhood would be octopi, of which we know very little besides the fact that they're frighteningly clever and bizarre. How does one even begin to understand the thinking of a creature whose brain is decentralized into each of eight tentacles? We can guess that if they're capable of numeracy, their conception of numbers would be base-8, but beyond that there's not much else to go on in speculating. They're pretty accurately summed up as "aliens among us." They're not especially social creatures, so that makes communication much less likely, but still - they're obviously smart enough that they deserve not to be treated as a food source by humans.
In fact, where humans have a viable choice, we shouldn't use any animal life as a food source, but we do have to set priorities in how rapidly to move on implementing such a change and how stringently to enforce it based on the qualities of a given species. It may sound disturbingly like racial hierarchy to try to judge the sentience of one being from another, but it's unavoidable in changing the way humans have typically viewed other species. You have to start somewhere, and the best place to start are creatures that clearly deserve recognition. In fact, even without a lot of political progress, socially the arc of history has been continuously moving toward such recognition.
When you read 19th century accounts, they really did not have any conception of even higher mammals as having any intrinsic existence. Whales were just blobs of oil for the taking, furry creatures were just pelts for the taking, and that unthinking callousness translated to how humans related to each other as well. We still have lots of hunting, fur trades, etc., but it's now qualified - society sees it as something that isn't inherently legitimate. People who kill things purely for fun are seen as dubious characters, not intrepid adventurers, and that becomes more and more true the higher the animal involved.
Bears, for instance, were once slaughtered as if it were nothing. Now the attitude is very different toward them. You can hunt them in some parts of the country within stringent limits, but in many parts of the country if they were to show up in a city you're supposed to just let animal control tranquilize and relocate them - not shoot them. And in fact, in some cases bears have killed people and officials have basically ruled it the equivalent of justifiable homicide because the people were being stupid and the bear acted on instinct to defend its cubs. No revenge is taken, and the bear isn't killed to avoid future attacks because it did nothing wrong - it saw a strange animal it thought was threatening its offspring, and defended them. We empathize with the bear.
The moral insight in such an attitude is quite advanced. Even if there are no explicit laws granting animals rights - in fact, even laws against cruelty to animals restrict human behavior rather than recognize any intrinsic right on the part of other creatures - the very idea of such rights remains radical. The idea that other species have an intrinsic existence apart from their utility or threat to humans is radical, especially since a large segment of the human species still doesn't even understand or recognize the concept of rights at all, even in reference to other humans.
I like to imagine a future where every living thing - and perhaps, everything period - has nonzero rights, because everything contains at least a kernel of existence. Some judgment would have to be made about the relative value of a mosquito over a dog, or a mouse over a lizard - that's just unavoidable. But nothing should have zero moral value. Not even inanimate objects. We already somewhat instinctively understand the value inanimate objects can have with protections for natural features like rock formations, mountains, canyons, etc. And we also know that something is wrong if someone were to just break something for the hell of it - we know that's not a good thing, even if it's their own property.
Some day humanity will have a common respect for life and an attitude of tenancy toward the places we inhabit and the objects we create or buy. I personally have started to internalize this understanding, and for the past few years have avoided killing bugs except mosquitoes and spiders that look dangerous. Even when a fly is buzzing around my ear and driving me batshit, I think about the fact that it's not deliberately annoying me - it's just looking for food.
And why should I take its life for that? It's not a threat to me, it can't make the junk food I'm eating go bad, and its only crime is being annoying, and no living thing deserves to die for being annoying. A fly is not a person, clearly, but it lives and wants to live. So I leave it alone. Once the annoyance passes, I know leaving it alone was the right thing to do, and that feels good.
Some day we will live among other animal species as equals, learn things about them we never knew or even suspected, and develop cultures of which they are a part. Still other species we will leave alone and keep them isolated so they aren't harmed by us, though they may not be equals. And the rest we will at least learn to accept and appreciate as living things rather than seeing them as our property, or pests with no right to exist around us. Within that understanding, we will learn to see the life in everything - even the slow life of mountains, of entire planets, of stars, of the cosmos as a whole.