Here's my little insight on suggestions:
Fantasy
The Farseer Trilogy and The Tawny Man Trilogy - Robin Hobb
Well written set of books with great characterisation, character interaction, pacing and storyline.
Memory, Sorrow and Thorn - Tad Williams
Not even sure why I like the series, the story is typical to what you expect from a fantasy series, but they are superbly written, with rich background details and great world building.
Discworld books - Terry Pratchett
A read you have to experience for yourself. All books are very cleverly written and are never lacking in imagination, humour and wit.
The Children of Hurin - Tolkien
Aside from LOTR and The Hobbit, I feel this is one isn't given enough recognition. Personally I found the story excellent and if you've read all the background lore concerning the deep and vast Middle-Earth world the story here will tingle your lore taste-buds.
The Wheel of Time - Robert Jordan
Now I know this series isn't everyone's cup of tea but personally I'd recommend it to anyone who likes a meaty fantasy series. The first time I read it through I became disenchanted and a little frustrated once I hit about book 8 because it had slowed down considerably (and 10 was the latest one at the time). However upon a recent re-read I've picked up on things I had never had before and am much more appreciative of certain characters and Jordan's storytelling. Also the newer books got rid of many frustrations. Jordan certainly isn't the greatest of writers, but the series is nonetheless entertaining.
His Dark Materials - Philip Pullman
For a long time this was one of my favourite series. It's unique and highly imaginative, with some great characters and world building.
Sci-fi
The Foundation Trilogy - Isaac Asimov
The man is nothing short of a genius. I first read the books when I was a bit too young to appreciate them, but then a few years later I picked it up again and man what a read.
Gaunt's Ghosts - Dan Abnett
You were bound to run into it and so I thought I might as well show you the only author worth reading for this. This series is a Warhammer 40k series and follows the Imperial Guard. Dan Abnett is one of the few writers who's actually any good for a WH author. I particularly love this series as I'm a big fan of the extensive 40k world and the books follow "normal humans" in a world of many overpowering beings. Characters aren't safe and anyone can die in any way possible. If you take the time to read into the background of the universe you will find it's very rich and detailed and you become a little more appreciative of the books and their settings.