From another thread,
There are, however, a number of species trembling just on the verge of sapience so far as we can tell, held back by the fact that in their particular evolutionary niches, sapience wouldn't give them any particular advantages. Dolphins and chimps are the obvious candidates, of course, which is why those were the first two species uplifted by humans in David Brin's Uplift universe (and a good thing, too, as when we discovered the civilization of the Five Galaxies, it turned out that they didn't believe sapience could occur naturally, and your rank as a species was determined by who your Patrons were and how many other species you had uplifted. Humans have no known Patron race; what kept us from being forcibly adopted into a hundred thousand years of servitude by an older species was the fact that we had two client races of our own already). However, the behavior patterns of raccoons, corvids, and coyotes shows that they're also right at that ragged edge of becoming sapient.
It's an interesting thought experiment - if we humans manage to keep other life forms on this planet alive when we (seemingly inevitably) go extinct, who's the front-runner for the next sapient species on Earth?
If I may, I'd like to continue this thought without derailing the other thread.
Racoons are too well adapted for their niche, I think. The best thing in their favor is the likelihood that humans will alter their environment to the point where survival demands long-term planning and teaching of the young. In fact, I believe it was exactly this which created homo sapiens from Australopithecines. Around 2 or 3 million years ago the environment began to radically change as Earth began its long slow march into our current Ice Age. Forests became savannas, inland seas dried up, seacoasts moved out, in many places for hundreds of miles. Protohumans had to adapt.
Raccoons are adaptable, have hands, and can think and use makeshift tools. They also teach their young. I am not aware that they have cultures which differ from region to region.
Dolphins and other whales may already be sapient, but we're not smart enough to figure out their language. Dolphins are reported to have localized cultures, which is evidence of teaching young. Right Whales are song-writers, but whether there is meaning in their songs or if it's just a courtship behavior is unknown. We know the song evolves over a season and the next season begins with the song of the previous season, but why is a mystery still. (To us anyway. The whales presumably know what they are doing.) In any case, they'll never be technological species because they lack manipulating appendages.
Squid and octopuses might be contenders for the sapient league. Though trapped by biology to never becoming fire-users, they are known to have at least simple communications. There is no evidence they learn from one another, but octopuses have consistently out-smarted the humans who try to test their intelligence.
Rats are a contender. While not currently showing signs of sapience, they are adaptable survivors. Then there are parrots, especially African Greys and those chubby guys from New Zealand.
Scientists are learning every day that animal intelligence is far more complex than it at first appears. Fish migrate thousands of miles to enjoy a bounty of baby sea-birds learning to fly, somehow remembering a year later that the event is about to begin. Elephants appear to be born with a map of their lands including routes to watering holes and grazing. Coyotes and wolves famously cooperate with crows.
The animal kingdom is filled with surprising glimpses of intelligence, and which species becomes the next sapient one is open to debate. It may be that it's already out there and we don't recognize it yet.