{Read and own these} Eragon [+], Eldest, etc (very recommended) *
Brian Jaques
{Read some} Redwall series (some [+])
David Eddings
{Read and own these} First series: Belgariad (Pawn of Prophecy, etc) * [+]
Second series: Malorian *
Robin Hobb
First series: Assassin's Apprentice *
Second series: The Liveship Boats *
Third series: The Amber Fool * (name may not be correct)
Chris D'Lacey
??? series
The Fire Within (Green book)
Ice Fire (page blue)
Fire Star (Red)
Fire Eternal (Gold)
Garth Nix
{Read these} The Old Kingdom series [+]
Sabriel
Lirael
Abhorsen
{Read some} Keys to the Kingdom
{Read some} John Marsden: Any, but especially "Tomorrow, when the war began" [+]
Andre Norton and Mercedes Lackey
Halfblood Chronicles
The Elvenbane
Elvenblood
Matthew Reilly
Temple
Books recommended to Chanté
Sci-Fi
Isaac Asimov
Foundation series are good
The Robots ones are classic
Well-known for short stories; these usually have a twist at the end (which is what I think is required for a good short story)
"20th Century Discovery" is science, rather than sci-fi; just pick the chapters you like in this one
Arthur C. Clark; not all his works are sci-fi
"2001, a Space Odyssey" is the classic
John Wyndham
Day of the Triffids
E. E. "Doc" Smith
The "Skylark" series; I think the first is called "The Skylark of Space"; it's kinda dated (ie. no calculators invented yet), but the stories are still good
"Girl books"
Laura Ingalls Wilder (Ingalls is her maiden name, Wilder her married name)
"Little House on the Prairie" series (the first one is "Little House in the Big Woods", which is more children-oriented, but is still worth reading)
L. M. Montgomery
"Anne of Green Gables" series
Elanor H. Porter
"Pollyanna" series (some of the later ones were written by someone else)
Johanna Spyri
"Heidi" series (some of the later ones were written by someone else)
Dystopian
George Orwell; he's written a few classics, but the only one I've read is:
1984 (keep in mind that this was written before the TV show "Big Brother")
Desert Island
Johann Wyss
Swiss Family Robinson
William Golding
Lord of the Flies (but only after reading Swiss Family Robinson; this is also Dystopian)
Historical Fiction
Stephen Lawhead
"Taliesin" series
Francine Rivers
"Mark of the Lion" series; I think the first one is called something like "A Voice in the Wind"
John Buchan
The "Richard Hannay" series, starting with "The Thirty-nine Steps". This is a sort of adventure/spy sort of thing.
Fantasy
Raymond E. Feist
Riftwar saga (series); starts with "Magician"
Terry Brooks
Shannara series (starts with "The Sword of Shannara")
Anne MacCaffrey
The Pern series, starting with either Dragonsflight or Dragonsdawn, but they don't really need to be read in order
Alan Garner
The Weirdstone of Brisingamen
The Moon of Gomrath
Susan Cooper
"The Dark is Rising" series
Katherine Kerr
Daggerspell
Darkspell
Dawnspell: The Bristling Wood
Dragonspell: The Dragon Revenant
Other
Arthur Ransome -- the "Swallows and Amazons" series, starting with "Swallows and Amazons"