If humans didn't exist, what species would populate the earth? Would an animal gain human-like intelligence if humans weren't here? What animal would gain dominance?
Originally a North-American species, it has dexterious hands and thumbs, can stand upright not unlike a meerkat, is an omnivore, good at problem solving and has a complex social life. These are all traits that have been proposed as crucial for the development of Homo Sapiens.
Without human existence, present-day North America is full of large herbivores, with descendants of mammoths traversing the arctic from Scandinavia through Siberia and Canada. The Raccoons spread north and live on a mixture of scavenging on large prey and hunting down smaller or weaker prey in packs. Without human interference, the next glacial period arrives when it should and allow the Racoons to cross the Bering Strait. From there they spread rapidly throughout Asia and Europe.
In Europe they become a terrible invasive species, decimating birds, amphibians and other mammals just as they have done to a lesser extent in real-world Europe today. A line of Racoons radiate out on open grass-land, either in central Eurasia or Africa and develop a truly upright posture, to better survey the land for prey and predators. This frees up their already dexterious hands and sets off a feedback-cycle between tool-use, more dexterious hands, brain development and hunting techniques.
One sunny day, a million years from now, a young inquisitive racoon is left back in camp while her family hunts. Out of curiosity or boredom, she grabs a piece of flint and slams it against a rock laying in the dry grass...
Simplified, social behavior in animals demands more brain power for memory, communication, and interactions. Who is the leader? Is Jack watching for enemies? Bob is mad at me for stealing his food.
As early hominids evolved to keep track of many members of their 'tribe,' they evolved ever-larger brains to cope with the demand.
However, social behavior alone isn't a guarantee to evolving a dominant position on the planet. There are many social animals which are quite intelligent, but obviously have not achieved the same status as humans.
Intelligence can be a naturally selected trait for solving problems, and ultimately survival. There are many theories on how human intelligence came to be.
If humans' ancestors had not existed, it's possible a different type of hominid would have risen up—literally—to take our place. Some theories of human intelligence link bipedalism, at least in part, to our success.
Perhaps one of the "most intelligent" animals on the planet would have found a niche without humans present, and evolved even greater intelligence, becoming dominant. The list frequently changes, but among them are:
Perhaps it would take another few hundred million years for dolphins to become what you would consider dominant. (Perhaps that is happening anyway!)
If humans had not evolved, it's possible no other animal would ever evolve human-like intelligence. It's difficult to say if humans' presence has somehow had an effect that caused another species' intelligence to cease being a favored attribute in natural selection.
Perhaps instead, we are a catalyst for hastening the rise of a smarter species than ourselves. It may be only millennia, you see, before all the dog training we've taken part in, becomes our undoing.
In terms of non-great ape animals (which I assume is not what you want, since they will basically just evolve into something that is, well, more or less like humans, probably… unless you're going for a Planet of the Apes-type vibe) I believe that African grey parrots are probably the closest in terms of having the “full package” towards intelligence, including a decent ability to manipulate their surroundings with their talons, with the added benefit that they can also fly! They're not quite there in terms of being able to use tools, but in terms of everything else, they're close to being “sapience-ready,” I think.
The other contender, often overlooked in my opinion, is the cuttlefish. They have a surprising number of highly-advanced mental capacities, especially considering that invertebrates are often thought of as being universally far less sophisticated or “less evolved” than vertebrates, and they have their tentacles that they can use to pick things up and move them around… plus, if you go with the cuttlefish, you can have them evolve into a Cthulhu-like or Illithid-type race, which is a cool trope, I think!
There are lots of different theories about what aspects of a creature push it more towards overall “intelligence,” as we would probably define it in a worldbuilding context. Social behaviors and ability to manipulate one's surroundings are two of the most important ones, I believe.
Insects are sometimes viewed as currently dominant taxonomic group. They may have social behavior, hierarchies, bees can communicate each other the location and build relatively complex structures like honeycomb. These families may be superior to human families as they consist of big number of adult, fully capable individuals, not just of two adults and children who cannot do much.
The only problem is the small size (so limited size of the brain), but say Hercules beetle may be 17 cm long so the brain need not be very small. Titan beetle is slightly shorter but has more massive body. The problem is probably that social insects are not as big as these beetles. Also, it may possible to have distributed brain built from brains of multiple individuals, using sound or electromagnetic waves to communicate. A bee brain contains about 950 000 neurons, human has about 100 billion. 105 000 bees would be required to have the same number of neural cells. That much can easily live in just two hives standing nearby (60 000 per hive) - fully realistic.
It may be only a question of time before the nature hits that opportunity.
By the definition given here: http://www.biology-online.org/dictionary/Dominant_species, any species' "dominance" is only relative to a specified environment. A variety of animals could be considered dominant to us in their natural habitats - though if we instead define "dominance" by our ability to dominate/subdue/kill other species in their natural habitats (this seems to be the definition used by the OP and most replies here), and thus dominate those habitats that we are not native to - then I would argue that there would not be a dominant species other than us.
If we humans were out of the picture, I don't know if any other species would exhibit our "will to dominate all life". on such a scale that we could consider them to be the globally dominant species. Other species tend to stay in their own habitats, and are not likely to be able to adapt or survive outside of them. Such dominance as we have achieved would certainly not be gained by another species quickly (much evolution and learning would be required), so while an interesting question to consider, I doubt we'd ever come close to guessing the species that would evolve to our level first. Who knows, maybe a bacteria would begin wiping out enough of the life on the planet such that it would become the dominant life form by overall biomass, overall prevalence, and kill-count.
I'm surprised nobody has yet mentioned rats. Just to piggyback on the reasoning of other answers, rats are social, intelligent w/problem solving skills, dextrous, and omniverous. When working together, much like we think primitive humans did, they can overcome a predator, and bring down prey larger than themselves.
Lots of neat answers here, but I would propose.. Troodude!
OK, I got that from a kids show, I don't even remember which one. It talks about a possible evolutionary progression from a particular Dinosaur called the Troodon.
The smart dinosaur theory puts forward that if they had survived the KT event, they would by know have evolved human level intelligence. The reasoning for this is that their brain in relation to body mass was unusually high. They had binocular vision based on eye placement. Their tooth shape suggests they may have been opportunistic omnivores. Their forelimbs could have easily turned into "hands" with manipulative digits.
More fanciful interpretations depict something that looks kind of like a sleestak from "Land of the Lost"
Who knows, If that little guy could have survived the KT, he may have eaten our most distant ancestors and supplanted us that way.
To slightly change the question, could an earth-like planet with slightly altered geographical/geo-historical features, themselves based on slightly different chemistry and thus climate and land-altering features, have a different dominant species? Moreover, if this species also evolved abstract science faster than we on earth and they sent astronauts to observe earth, what would this species and its proxies and assistants be? (I.e., human/dog/horse complex on earth)
I changed the question because I think a species like the feline, which clearly dominates every predatory food chain it has co-evolved with, is given short shrift on your list. Especially since otherwise worthless cats - we certainly don't breed, protect, pamper and give medical attention to cats anymore because of their rat-killing ability, in fact, that aspect of feline behavior is looked at with disgust by most modern "western" humans - are now the fastest growing mammal population worldwide, even surpassing racoons, which several of your contributors rightly pegged as another possibility.
To get to the point: a species that can enlist a species superior in some respects (let's say on their planets apelike creatures also developed spoken language) to work for them can't be counted out entirely. The ability to coerce or trick another species into helping them in very a one-sided relationship may be a better indication of evolutionary success than mere "intelligence", whatever that generalized concept means pragmatically.
Also, many niche species on earth that are not well known have developed fingers and even thumbs much like ours - certain rain forest tree frogs, for example. And the tentacles of intelligent octopi or other cephalopods could easily be surrogates for hands.
And the whole question of language implying a need for writing is also erroneous. Animals IMO can have as sophisticated a nonverbal language, based as mammals and birds clearly must be on visual images - mandalas, icons, emogees, whatever in human terms - and they could transmit knowledge and information via that language in many ways besides with fingers and thumbs.
They could have, as I indicated, if they ever needed a written language, have adopted hominid pets to do it for them, the way we adopted wolves for hunting help and horses and oxen for hard work. ( My cat forced me to write this. Actually I think dolphins are the best choi ...
I see several answers for this, so I'll list them off.
*If only humans are taken out of the picture, then I believe it would be another hominid species, like Neanderthals, who would not have had to deal with competition from Homo Sapiens.
*If by humans you mean homonids, I believe that cephalopods would dominate the sea and either avians or felines would have dominated the land. Then, depending on how fast their intelligence grew after naturally dominating their habitats, it would either be a world of squids, cats, or birds. Or maybe evolution pulls something out of left field and we get talking horses instead. Who knows?
I think that "dominance" should be defined better, especially because it seems to be direclty linked to intelligence. It's true, we are dominant because of our intelligence but it's worth to underline that we are NOW dominant because of intelligence AND ESPECIALLY TECHNOLOGY. (a physic professor won't be really dominant if left naked in the savannah) We are dominant all around the world because of the same reasons. Dominance and intelligence are not welded together, we evolved a lot because intelligence (our main power) was/is the best tool at that/in this era. We didn't do anything "special", we didn't actually choose to be intelligent rather than strong or poisonous, it happened to be the best option and we came out on top of the food chain.
If the earth situation/climate is more or less the current one, and if by dominance we mean superior intelligence/technology, i'd go with primates or racoon as other people already explained. Otherwise, the question is not complete enough to be answered.
If "dominance" is defined by which kills off the other, then.... Whatever virus, bacterium, or fungus that (largely) kills off humanity. A future gen of a highly deadly virus like Ebola that's evolved to be airborne and thus highly contagious*; or a highly contagious antibiotic-resistant bacterium. Predicted to happen in the next few centuries.
*we've been lucky that most past microbes have been either deadly or contagious but not both. When one evolves that is both, watch out: see http://www.businessinsider.com/how-contagious-is-ebola-2014-10
If by "dominance" you mean using your own intelligence, strength, mobility etc., then I don't know. But if by "dominance" you mean usurping these abilities of other species if you don't have them yourself, and controlling these abilities of other species to further your own agenda, then the answer is GRASS. What other organism has made itself so valuable to (an)other species that it uses the strength of others to clear forests to give it more living space (all the grain grasses), the intelligence of others to ward off predators/pests and to provide more nourishment (same grain grasses benefitting from pesticides and fertilizer), and even the visual/tactile tastes of others to rip up whatever else was there before and roll sod over it (your good old front lawn)?