If that most wondrous of all human creations - a child - is never more to roll and play on the green Earth, then what really would be left of us?
What of our spirit might be truly immortal?
What will remain of our greatest creative forms of human expression?
One day, perhaps, we will learn to control our appetites, or our duplication rates.
More crucial to us still here on Earth, right now, is whether we humans can make it through what many scientists call this planet's latest great extinction - make it through, and bring the rest of Life with us rather than tear it down.
The natural history lessons we read and understand in both the fossil and the living records suggest that we can't go it alone for very long.
Medical Errors still growing, review link http://theinnozablog.blogspot.com/2008/03/medical-errors.html
WARNING: Following discourse is for religious inclined readers only. Atheist (or Earthiest) or free-thinker are welcome to explore too.
Various religions offer us alternative futures, usually elsewhere, although Christianity, Islam, and Judaism (in alphabetically order only) mention a messianic reign on Earth lasting, depending on whose version, somewhere from seven to 7,000 years. Since these would apparently follow events that result in severe population reduction of the unrighteous, this might be feasible.
However, since these three religious disagree about who are the righteous, to believe any one of them requires an act of faith. Science offers no criteria by which to pick survivors other than evolution of the fittest, and into every creed are born similar percentages of stronger and weaker individuals.
As to the fate of the planet - Earth and its other residents after we're finally done with it - or it's done with us - religions are dismissive, or worse.
The post-human Earth is either ignored or destroyed, although in Buddhism and Hinduism, it starts again from scratch - as does the whole universe, similar to a repeating 'Big Bang theory.'
The correct answer to whether this world would go on without us is : "Who knows?"