Although here are many great science fictions that are technically about the future many of them are so far in the future that they have no connection to our world and others are so different from our world that they have little or nothing to do with our future. If you eliminate these you get a far shorter list.
Perhaps the most famous book about the future is "1984" which is ironic since the date is no longer the future, but the ideas that were put forward in "1984" are still relevant to today. And though "big brother" has turned into little brother questions of security, government control and more are still important.
Also an excellent warning of a possible future is "Fahrenheit 451". Set at some nebulous future date this is a world that declared war on knowledge. Considered a story about censorship Bradbury says that it is a story about how television devalues knowledge and context. Either way it is still relevant to our modern world and a future we may see.
Perhaps the most accurate writer about the future was Jules Verne and one of the most surprisingly accurate was "From the Earth to the Moon". Written in 1865 Jules Verne tells a story of a spaceship launched from America with very capsule very close to the size of Apollo. It had a crew of three and was launched in 1961 from Florida.
As a more modern book "Snowcrash" by Neil Stephenson is set in an America that has broken into small city states run by corporations, churches, even the mafia. The story has numerous technologies that are reasonable extensions of technology that currently exist. From military to a virtual reality internet this is a story that is connected to our past and shows a possible future. "Diamond Age" also written by Stephenson is also an interesting examination of a near future with technology that is changing things.
Finally, there is "The Time Machine" by H. G. Wells. This story goes into the distant future, but by introducing the idea of time travel to science fiction it has opened up a wealth of stories about a closer future and created one of the most popular ideas in science fiction.
Science fiction is generally thought of as a genre about the future and though many of its books are set in the future many of those futures have no connection to our own time. These epic science fiction book have governments of empires, and citizens who don't even remember the earth, yet a few book do focus on what might actually happen. These real possibilities are often scarier than anything the other books could hold and at their best can even help to prevent worlds we would not want to live in.