If Humans Went Extinct, Would Something Like Us Evolve Again
I've seen the question that's the title of this entry many times, most recently on Quora (If all humans died, would we evolve again from apes? and in a comment thread to Aaron Weyenberg's answer to If humans evolved from apes, why are there still apes?. I wrote a response for Quora that I figured I'd adapt for the blog.
It's certainly possible that some lineage of modern ape or monkey could eventually evolve into something like humans (though definitely not exactly the same as us), or given an even longer time, some other lineage not particularly closely related to humans could as well, but it seems extremely unlikely.
The first issue with the question is an assumption I've pointed out before (such as in the entry, Local Church Misunderstands Evolution - Why Are There Still Apes?). This assumption goes back to the Great Chain of Being, that there's a hierarchy of life, with humans at the pinnacle being the most perfectly evolved of all creatures. That's simply not the case. Evolution adapts organisms to their environments. The raw material for this is random mutations, with natural selection acting like a filter to ensure that only beneficial and neutral mutations persist (though that's not the only mechanism in evolution). There's no intention behind the mutations, guiding organisms towards some end goal. It simply adapts them to their current environments, with no foresight to some future species.
Moving on, there is a concept in biology known as convergent evolution. This refers to two separate lineages that didn't originally have the same features both evolving those features independently, 'converging' on the same solution. And it is true that convergent evolution happens quite a bit. Here are a few examples showing how different marsupial and placental mammals have independently evolved similar body types.
But convergent evolution is almost always in cases of 'easy' solutions. Let's look at an example separate from those above or from humans - powered flight. Powered flight has only evolved three times in vertebrates (each time by a different path - pterosaurs, birds, and bats), because powered flight is a difficult to achieve strategy. It takes a very specific set of adaptations, and the likelihood of all of these adaptations occurring simultaneously in a single organism is rather small. If birds and bats were to suddenly go extinct, it might be quite some time before another lineage evolved to fill that flying vertebrate niche.
Just focusing on the intelligence aspect of humans, when you look around at other animals, the type of extreme intelligence seen in humans just isn't very common. On land, there are the other apes and elephants that are nearly as smart as us. In the water, some dolphins and whales also approach human intelligence. But none seem to be as smart as us, or at least not in a technologically inclined way.
There's a reason for that. Brains take a lot of energy. Even though your brain is only around 2% of your weight, somewhere around 20% of the calories you eat go to supporting your brain (one source: University World News: The brain - Our most energy-consuming organ). That's a lot of extra food you need to survive compared to a similarly sized animal with a smaller brain. And yes, being clever can help individuals exploit more resources than less intelligent animals, but just by looking at the distribution of intelligence of all the species out there, it doesn't seem like a strategy that natural selection often favors.
Even us humans, who are now so dominant on this planet, wouldn't have looked particularly noteworthy a few tens of thousands of years ago. Genetic studies show that the effective population got all the way down to around 10,000 - 30,000 individuals at some point in the past (more info: Why Evolution Is True: How big was the human population bottleneck? Another staple of theology refuted). That's not a very successful species. Our ancestors were on the brink of extinction, and barely managed to survive.
If some modern lineage of apes or monkeys went down the evolutionary path to extreme intelligence with the high energy requirements of large brains, they might not be lucky enough to survive a similar situation to what caused the bottleneck in our ancestors, and might end up going extinct before their culture advanced to the point where technology made them as successful as us.
Once you start considering the other specializations of humans (bipedalism, long distance running, object manipulation, etc.), the possibility of another lineage evolving into something closely resembling us seems even more unlikely.
Image Source 1: Wikipedia, with further editing by me.
Image Source 2: The Roaming Naturalist, who herself doesn't know where the original came from. Let me know if you recognize it.