OP - There are many different kinds of SF recommended on this thread. Here is a short overview of the genre imho, and some recommendations:
Sci-fi used to be about space travel, first contact with other races, colonies, etc (around the time that man went to the moon). Here is some classic sci-fi that has survived from those days:
Dune - Frank Herbert (Consistently voted #1 sci-fi of all time, although it is published in 1965)
2001: A Space Odyssey - Arthur C Clarke (Brilliant story, a true classic)
The Foundation (series) - Isaac Asimov (Interesting premise, another classic)
I really like Philip K Dick. It is not the kind of book where the beauty of the prose blows you away, but the ideas are incredibly original and he was a genius imho. I'd recommend his short stories (including Minority Report, We Can Remember It For You Wholesale (= Total Recall), and his books Do Androids Dream Of Electric Sheep (= Blade Runner), A Scanner Darkly, and Martian Time-Slip. In each, you will find that the book is much better than the movie.
This fantastic book, I would say, is a bridge between classic sci-fi and new generation sci-fi that builds on internet technology:
Hyperion - Dan Simmons (Named after the poem by John Keats, the book refers quite a bit to Keats. Interesting and poignant, it is considered one of the best sci-fi out there. And it's an easy read.)
New generation sci-fi that deals with the near future on this earth, how things change with technology that we already have (internet etc) or are about to have (nanotechnology, etc):
Neuromancer - William Gibson (The book that started cyberpunk, where Gibson coined the term 'cyberspace'. If you like it, Gibson has written several more in the same vein)
Snow Crash - Neal Stephenson (No doubt one of the best sci-fi ever, impossibly connecting ancient Sumerian myths with programming languages, hacking the brain, etc. Impossible to explain. Time magazine chose it for its list of 100 Best English-Language Books since 1923)
The Diamond Age - Neal Stephenson (One of my favourites, about the day after tomorrow, when nanotechnology is everywhere. Social structures have significantly changed. Little girl finds a high-tech educational book that interactively educates her and guides her intellectual development through the years. Fascinating discussions about politics, society, morals, and pretty much everything else.)
Some recent books that were most impressive in their breadth, scope, and incredible world-building in detail:
Seveneves by Neal Stephenson. The moon shatters and people realise that the Earth is doomed. How best to plan for the centuries ahead to keep the human race alive? Brilliant book, meticulously constructed.
The Three-Body Problem & its 2 sequels by Liu Cixin. Written by a Chinese author and translated into English, these three books are nothing like you have ever read. They are philosophical, scientific, and incredibly ambitious. Anyone with any interest in SF must read them at some point.
And a lighter read:
Ready Player One - Ernest Cline. Everyone in the world is playing this one game where keys to immense riches have been hidden. It's a fantastic puzzle, being solved bit by bit, with loads of 1980s cultural references)