Sci-Fi is my favorite genre. These are my suggestions in no particular order,
1) Anything by the grand masters:
Isaac Asimov
Robert Heinlein
Arthur C. Clarke
Ray Bradbury
2) James P. Hogan
One of my personal favorites. He does hard science fiction. The kind where the fictional science is almost believable. I own all of his books and it would be difficult to pick a favorite. Some that come immediately to mind are "Inherit the Stars", "Thrice Upone a Time", "The Genesis Machine", "The Two Faces of Tomorrow"
3) Frederik Pohl
The Heechee Series is a great read starting with "Gateway" which won both the Hugo and Nebula awards sometime in the mid-70's
4) Frank Herbert
Dune.
If you haven't already, then at some point you must read this. It is a bona fide classic. Period.
5) Orson Scott Card
The Ender Saga starting with "Ender's Game"
6) William Gibson
The Sprawl Trilogy starting with the classic "Neuromancer". I believe "cyberspace" was first coined in this book, and there is also reference to "the matrix - Mankind's unthinkably complex consensual hallucination representing cyberspace"
7) Anne McCAffrey
She writes good stories and her lead character is female, which is a switch from most scifi. I'd recommend anything in her Dragonriders of Pern series starting with "Dragonflight". I'd also recommend her Crystal Singer Series starting with "Crystal Singer".
.. that's just for starters. I have about 700 sci-fi novels in my personal library. I won't list them all for you! :)
On the Fantasy side
1) Everything by Tolkien
2) The Chronicles of Narnia by C.S. Lewis
3) The Thomas Covenant Chronicles, The Unbeliever by Stephen R. Donaldson starting with "Lord Foul's Bane"