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On the Sci-Fi front, I only have two recommendations (I've not read as much SF as I would like):

- Dune by Frank Herbert - widely considered one of the best SF books ever published.
- Ringworld by Larry Niven - again, considered to be very good. One of SF's classics.

Oh, mustn't forget The Hitchhiker's Guide to the Galaxy by Douglas Adams, but who hasn't read that?

Fantasy books, on the other hand... well, I've read hundreds! A few off the top of my head:

- Anything by Terry Pratchett in his Discworld series. I started with Wyrd Sisters. The series starts with The Colour of Magic (if you've seen the two-part film with David Jason, forget it - the book is far superior).
- One of my favourite series at the moment is Steven Erikson's Malazan Book of the Fallen (starts with Gardens of the Moon). You've got to be in the mindset to read it, because it is a bastard to get in to (though I had no troubles). The series as a whole is slowly growing to a close, and is a fantastic example of epic fantasy. It also bucks the trend in that it's not all castles and elves and orcs. You might prefer George R. R. Martin's A Sword of Ice and Fire.
- Walter Moers is a nice example of crazy imagination - The 13 1/2 Lives of Captain Bluebear, Rumo and City of Dreaming Books (he's got a fourth out soon).

I'm not sure which genre it falls under (Sci-Fi, possibly), but Flowers for Algernon by Daniel Keyes is supposed to be very moving, and a definite one to read if you want your view of the world thrown out of kilter.