How about this one, then?
That one proves that dolphins will respond if you play something that sounds like their call back to them. It doesn’t say anywhere that they use that sound as a name to identify themselves, or that other dolphins use it as an identifier, just that the dolphins responded when they played a sound made with a synthesizer that sounded like one of the sounds the dolphin makes.
I’ll have to introduce you to my sentient, self-aware dog and parrot!
Seriously, the few researchers still trying to prove dolphin intelligence have been grasping at straws for a couple of decades now. It would be nice if they were intelligent, but you’d think we’d have some better proof by now if they were. So far nothings been demonstrated beyond what’s capable with other clever, trainable animals.
I vote for kitties, because my house is already run by feline overlords. I assume with us out of the way there would be no stopping them. 
Harrumph! We’ve got video of octopuses opening jars. Sometimes I can’t even do that.
And walking. We’ve got video of them walking along the seafloor.
And I saw these Japanese prints where …
If the ability to slumber has any advantage in the new age, I’m going with the beagle.
Dougal Dickson adresses this in After Man and The Future Is Wild. I’ve read After Man, but haven’t been able to get hold of a copy of Future. However, I have seen the Discovery channel special based on it. After several geologic eras worth of climactic changes, continental drift and other species evolving and becoming extinct, Dickson thinks that a lot of coastal arboreal and ground niches will be available. His vote for the next inteligent species-
The tree octopus! The octopus already has inteligence (it can open jars of sardines, wait for closing time at the aquarium and sneak into other tanks then return to its own). It can survive for brief periods out of water. The tentacles can move it across the ground and are great for climbing.
Keep in mind that even in geologic time, Dickson expects the rise of the tree octopus to take a while.
My Vote- What animal could benefit from manual dexterity and intelligence? Cockroaches, rats and elephants all seem to be surviving fine as is. IIRC Roaches have barely changed since dinosaurs roamed the earth. They don’t need hands or a bigger brain. In fact, a bigger brain would just waste resources.
Dolphins Evolve Opposable Thumbs: ‘Oh, Shit,’ Says Humanity.
My vote for intelligent, tool-using builder species goes to the members of Procyonidae and Ursidae, particularly the Common Raccoon and the American Black Bear. (This is assuming that we’re excluding existing primates from the running.) I’d like to vote for order Octopoda as a runner-up due to their high intelligence and problem-solving abilities, but owing to the lack of internal skeletal structure, low-energy hemocyanin respiratory medium, and inability to effect oxidation or other high energy chemical reactions I find it unlikely that they’ll evolve beyond their aqutic medium.
The elephant has a good memory, but not an especially high level of analytical intelligence. That, combined with the amount of time they have to spend foraging to feed their herbivorious metabolism and their lack of adaptability to other environments would seem to proclude the from advancing.
The dominant species on the planet, though, are single cell bacteria who will demonstrate this at will if you are so unfortunate as to eat undercooked meat or contaminated vegetables. I guarantee Newton didn’t add anything to the library of human knowledge while doubled over with dystenery. He also couldn’t digest anything without them, demonstrating that intelligence is an overrated (and as yet unproven) measure of evolutionary superiority.
Stranger
Why are we assuming that something else has to become intelligent? It seems to me that the vast majority of species did not evolve towards more intelligence. The earth’s biosphere existed for billions of years without something as intelligent as man on it. If man vanished tomorrow, I think it’s entirely possible that Earth will just chug along the way it is, except without humans. Animals will move into the ruins of the cities, and life will continue to evolve. If another species becomes intelligent, it’ll be because whatever environmental conditions exist caused it to select for intelligence. And we have no idea what that might be until it happens, because it’s kind of chaotic.
Parrots. Manual dexterity, intelligence, they’re social and they can fly. 
I, for one, welcome our new elephant overlords.
Another vote for the racoons.
Squids? No aquatic species is going to evolve sentience unless it moves onto land. (If whales had hands, what would they do with them?) And squids would have to evolve some bones to make it here. There’s a reason you don’t see them on land. Well, except for the delectable, farm-fresh prairie squid! 
WARNING: Do not neglect prior debeaking!
“Manual dexterity”?
By what other standard can we define any one species as “reigning” over the Earth? If it’s just a matter of survival and reproduction and species-longevity – there’s just too many candidates to choose from, starting with bacteria and working up to thousands of insect species. If it’s a matter of being at the “top of the food chain,” there’s at least one candidate species in every local ecosystem. But humans “reign” over the Earth because we can do anything we want to or with almost any other species, and it’s only intelligence that makes that possible.
From [url=]Friday, by Robert Heinlein (Friday’s boss has asked her to come up with ways to prevent the next Black Death outbreak or at least prevent it from spreading to the space colonies):
But with us out of the way, there’d be no one to open the cat food for them.
I vote for opossums.
A back-country farmer named Hollis
Used snakes and oppossums for solace
The offspring had scales
And prehensile tails
And voted for Governor Wallace!
– Isaac Asimov
It was determined years ago:
:dubious: A link to this post will be forwarded to Stephen Colbert!
I’m not going to bother to look up the exact wording, but it’s one of my favorite wisdoms from The Master, something along the lines of: cockroaches have been along much longer than we have and there are many, many more of them; and they’ll probably be around long after we’re gone. Thus, we might reasonably inquire, just whom is infesting whom?
[shrug] They need us and we don’t need them.