An Extremely Important Point To Remember
Sapience does not include knowledge or higher intelligence.
Most people, when thinking about sentience or self awareness, automatically include high intelligence to come with it as a combined package. This assumption is incorrect. We (humans) have some very dumb individuals in our society who are barely socially functional at all. Yet they are as much conscious about themselves as the rest of us are.
Now as far as self awareness goes, probably most mammals are already self aware. Many mammals have enough brains to overcome their natural drives and plan their actions by the best of their experience and skills. Dogs (specially German Shepherds) and dolphins are prime examples of that. Also don't forget the chimpanzees.
Another thing which does not come with sapience, is knowledge. When people talk about some animal gaining human level self awareness, they automatically also think they would have all the knowledge of human inventions, communication and social structures. This is not the case.
For example, a herd of wild buffaloes will only charge directly at human populations when given a motive. They would not go planned and take out military outposts at night and block the roads with jammed vehicles (dragged to the road).
Which Creature Has The Best Chance Of Defeating Humanity?
If human-level knowledge is available to the creatures, then it is definitely going to be mosquitoes. Once they have the intellect and the knowledge of the diseases they are able to spread, there's no stopping them!
At first, all of Africa will be swept clean by the pandemics of malaria, dengue and yellow fever. Arabian peninsula, Asia, South America, central America, parts of Europe and most islands would follow. While humanity will survive in far north and south, the global dominance of humans would end within a decade, if not just a few years.
Wasps and hornets also have an amazing chance at this. However, intelligent wasps would not go on an all-out war with humans and ring the alarms immediately. Instead, they would first multiply in numbers and then begin to invade suburban homes at night, one after the other. When hornets charge a house, it will be a silent, but extremely horrible raid. A thousand hornets raiding sleeping occupants of a house one night. Every human individual will be stung by 30 or more of them. Eyes, hands and throat will be the targets of stings. This will impair the ability of the target humans to:
- use cellphones to call for medical help
- pick up and use any available bug spray
- breathe (with swollen throats, breathing will be extremely hard)
The morning will see corpses of horrific corpses laying around in a suburban house. It will send a wave of panic in the region, but it will only help the hornets. They will make their hives near or inside human houses so that aerial spraying of insecticide no longer remains an option. They will continue to take one locality after another until the social structure collapses and all technological advancement is reversed. Once again, humans will be able to survive in extreme latitudes, but their dominance over the planet would be over.
Rats could have had a chance, if we were living in early 20th century, but rats (or any other mammal) holds no chance. Rat holes can be easily sealed and they can be easily starved to death by keeping all food items locked and not letting them feast on wasted food scraps. Cats too, do a great job of eradicating rats from a household.
Dogs might have had a chance. But there are just too few of them. And once humans understand the threat they are facing, we would quickly and easily eradicate all of them with guns and helicopters and whatnot.
Hares could have a chance by destroying all crops worldwide and throwing the human population into a global famine. However, I wonder if hares would survive after feasting heartily on pesticide-riddled crops we have. Also, we have a good chance of eradicating feral hares with airguns, traps, hunting dogs and poisoned baits.
All in all, I think only some species of insects (or arachnids) have the potential of launching human genocides and ending their reign of planet Earth.
Edit To Add: The Killing Potential Of Mosquitoes
Some members have suggested that mosquitoes are not as much of a threat as has been declared in this answer. And that mosquito-borne-diseases have a low mortality rate.
Remember that mosquitoes already kill around 725,000 people each year. A total of around 0.2 billion people are temporarily debilitated by malaria alone. And this is for mosquitoes which do not have any self awareness and their brains have a far lesser intelligence level than a cheap cellphone.
The diseases spread by mosquitoes include, but are not limited to malaria, elephantiasis, yellow fever, dengue fever, zika fever, chikungunya fever, polyarthritis, Rift Valley fever, Ross River fever, certain kinds of encephalitis and West Nile fever.
Members claiming that mosquitoes are easily contained and exterminated should keep in mind that West Nile virus was accidentally introduced into the United States in 1999 and by 2003 had spread to almost every state with over 3,000 cases in 2006. (source). And then again, this was for mosquitoes with no sapience (as we think) and almost no intellect at all.
Mosquitoes with self awareness and social communication skills have the potential to virtually wipe out human population from their entire areas. First stage would be to multiply by at least 10 times. The second stage would simply be to infect as many people with as many diseases as possible.
The initial death toll would be around 300 million people, if not more. Furthermore, mosquitoes not only spread diseases to humans alone, but also infect cattle and other pet animals. Also, no combined, urgent, international team would be formed against this deadly threat because the governments would never know that it is not a natural mosquito infestation, but an extremely potent attack by mosquitoes.
In case of vertebrates, it would be immediately known that they are working cohesively against us (humans) and this will help making focussed decisions easy. On the contrary, even if humans do learn that mosquitoes are working collectively against us, it will take at least several years (maybe a decade), during which the losses would already be irrepairable.