OK, here it goes:
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.)
Ready Player One - Ernest Cline (Brilliant new find of the past year (for me). 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)