A few that I like:

Flinx Series by Allan Dean Foster
Mid World by Allan Dean Foster (Lost of similarities to Avatar, I wonder of Cameron "borrowed" some ideas from this book)
Moving Mars by Ben Bova
Out of the Silent Planet, Prelandra, and That Hideous Strength by C.S. Lewis
Just about anything by Heinlein, but some I like are: Space Cadet, Farmer in the Sky, Tunnel in the Sky, Between the Planets, Starman Jones and Orphans of the Sky.

If you like short stories, With Friends Like these... by Allan Dean Foster is a hoot. Especially the story with the same title as the book.

My wife uses Ender's Game by Orson Scott Card to get her high school kids to read. If you are not a fan of SF, this might be a good one.

Agree on the Alan Dean Foster and the Heinleins...Two classics of SF from their respective era's.

The Moon is a Harsh Mistress IS IMHO opinion what classic hard SF is about

David Drakes Hammers Slammers are excellent modern Military SF.

Asimov and Clarke are must reads.

If you love long political and Imperial drama...the Dune series.

Those will get you a good start and some fine reading

To answer your question tho

ONE book..The Moon is a Harsh Mistress. R A Heinlein
Series The Commonwealth Series by Alan Dean Foster.

The Time Machine by HG Wells and the Time Ships by Stephen Baxter are a good pair of books linked together (the Time Ships is written as a sequel to the Time Machine - and puts a whole new twist on the classic story).
The Dragonriders of Pern is definitely a very interesting series, which, if you read the stories in chronological order go Sci-Fi to Fantasy to an even Sci-Fi/Fantasy split (and, as such, may be a good starting point for the avid Fantasy enthusiast). Also by her are the Acorna series and the Space Pirate series, both of which are quite enjoyable.
The Mars Trilogy (Red Mars/Blue Mars/Green Mars) by Kim Stanley Robinson is also a good trilogy, with very interesting characters in a fairly hard sci-fi setting.
Finally, I'd recommend the absurdist scifi trilogy (consisting of 5 books by Douglas Adams and one by Eoin Colfer - yes, it's that type of series) The Hitchhiker's Guide to the Galaxy. From interesting characters in absurd situations, absurd and semi-random notes about the Galaxy that are sometimes outright bizarre (never forget your towel!), and descriptions that are bizarrely unique ("They hung in the sky in exactly the way that bricks don't..."), it's definitely a series well worth reading.
Magius out.

A second for The Dragonriders of Pern. Parrallel Earth Resources Negligable.

Rendezvous With Rama by Arthur C. Clarke is very good as is the followup Rama II

Lucifer's Hammer by Larry Niven and Jerry Pournelle is very good. It is about the aftermath of a comet strike on the Earth.

Footfall by Larry Niven and Jerry Pournelle is very good too. That was one heck of a propulsion system.

H. G. Wells and Jules Verne are always good reads. It is amazing how much the stories have been changed for the movies based on their stories.

For science fiction, I would recommend anything by Philip K. Dick, but especially Ubik (it was the first novel of his that I read so it holds a special place in my library).

I personally really dislike Heinlein's works and would not recommend them but I agree with the others that Alan Dean Foster's Flinx series is a good read. Also worth digging out is With Friends Like These which contains the story 'Why Johnny can't speed', which is one of the stories that inspired Car Wars.

Perhaps a couple anthologies would help you find the niche of sci-fi that you could really get into. The stories are shorter but your exposure to what is out there would be greater.

I would also suggest that you avoid hard sci-fi in the begining (the in depth tech) and just concentrate on the flavor of sci-fi (the stories) that attract you.

It is wonderful that you are willing to give the genre a chance.

I would echo the folks who like Heinlein, but moreso for his earlier works (the 'juvies') like Tunnel In The Sky, Time For The Stars, Have Space Suit Will Travel etc. Also personal favourites include Starship Troopers and Glory Road.

I'm surprised nobody mentioned Joe Haldeman's The Forever War yet, that's certainly a classic. I'm also a huge fan of the original Dune book from Frank Herbert. Of recent works, I like Stephen Donaldson's Gap series.