Lots of great suggestions, I'll toss in a few I haven't seen mentioned or were just touched on. Leans heavily to military sf and sword and sorcery fantasy, 'cause that's the way I like to game:
anything by C J Cherryh - ranges from fantasy to military sci-fi. I especially like the Alliance Universe stuff - from Downbelow Station, Cyteen, Chanur's series. I only read about half the Foreigner series, that's up to like 15 books now - I like her earlier stuff a bit better. Great writer who makes you care about the characters, pulls you into the story and keeps the action moving.
http://en.wikipedia.org/wiki/C._J._Cherryhanything by Lois McMaster Bujold - sci fi 10 or so books in the Miles Vorkosigan series, these are a lot of fun. Richly detailed fantasy stuff with the Chalion series.
http://en.wikipedia.org/wiki/Lois_McMaster_Bujoldanything by Elizabeth Moon - good military sci-fi with the Families Regnant stuff and some good fantasy series too:
http://en.wikipedia.org/wiki/Elizabeth_MoonJohn Scalzi - Old Man's War series
http://en.wikipedia.org/wiki/John_Scalzi - these were great military SF.
Greg Bear - mind blowing universes - try at least Forge of God but again I haven't read a bad thing by him.
David Weber - the Honor Harrington series - Horatio Hornblower in space (that's actually a pretty good series too - not quite as rich as Master&Commander but HH (by CS Forester) and Bolitho (by Alexander Kent) used to be the 2 "go to" series for Napoleonic naval war fiction). Anyway, Weber is not nearly as good a writer as any of the above, some fairly contrived stuff, but it's still among the best military SF and is great to get inspired to fire up something like Aurora (mechanics based REALLY heavily on Weber's Starfire series).
fantasy -
anything by Harry Turtledove - lots of different fantasy series/one-offs
anything by Raymond Feist - great fantasy stuff - I saw one book mentioned above, I've read about 4 of his series and all were solid, esp. Riftwar.
anything by Fritz Leiber - CLASSIC fantasy, one of the pioneers. esp. the Fafhrd and the Mouser series, still one of the best ever.
older stuff:
Joe Haldeman - Forever War - classic, flip side of Starship Troopers. Follows a soldier through centuries of war due to time dilation during travel.
John Steakey - Armor - another great bleak story of a hugely put-upon trooper.
David Drake - Hammer's Slammers series - solid military sci-fi
Gordon Dickson - Dorsai series - ditto
Keith Laumer - Bolo series - giant AI armored tanks.
Fred Saberhagen - Berserker series - huge self-replicating robot space ships programmed to destroy all life.
Philip K Dick - every book is flawed but still great and weird. Basis for Blade Runner, Total Recall, Minority Report, etc. Man in the High Castle won a Hugo, alternate-history fantasy.
E E "Doc" Smith - classic space opera - Lensman/Skylark of Space - try one and see if you like it, it's definitely dated but still a great read imho.
Mervyn Peake - Gormenghast - Insanely detailed flavor, creepy fun gothic fantasy.
ER Eddison - Worm Ouroborous series -
ER Burroughs - I esp love the Mars series, bummer the movie was so bad.
Robert Howard - Conan! Awesome books.
HP Lovecraft - Cthulhu ftw - absolute must read.
Cordwainer Smith - each story is a jewel.
Other authors on my "go to" list - Andre Norton, Jack Vance, Poul Anderson, Roger Zelazny, Fred Pohl, Jack Williamson, Norman Spinrad, Robert Sheckley, Harry Harrison, Edgar Pangborn, Robert Silverberg, RA Lafferty, John Varley, Vernor Vinge, Bruce Sterling
Used bookstore tips - go in with your lists of authors in alphabetical order, try to buy series in chronological order (if you're JUST starting one and not familiar with it, you can usually figure out the order from the list of books by that author just after the copyright page, or from the ads for series on the last few pages). When in doubt, go for the earliest copyright date (but usually try for the latest *publication* date - some authors have revisions). When you like an author, get the rest of their bibliography from wikipedia/other sources. I list the books I have, by author, on 3x5 cards so I don't end up with duplicates. The more recent books are easier to get in to but alas the very best are hard to find in used books stores - that's why I list a bunch of older ones, so if you like "classic" sf it's pretty good hunting. For other ideas, look at lists of Hugo/Nebula winners and nominees, ha here's a site that lists winners of 11 different awards - still go to the individual lists to get the nominees too.
ED to fix the ONE name I didn't doublecheck :p