A Song of Fire and Ice by George RR Martin
So far there are three books in this high fantasy series, with a fourth on its way. Martin’s world is very medieval, with only hints at magic existing. The characters are very well written, with multiple points of view in each novel. This is by far my favorite fantasy series to date.

The dragons of the Seven Kingdoms all are dead and finally mad King Aerys is defeated by an alliance between the Baratheons and the Starks. A Game of Thrones begins when Robert Baratheon is still King. The long summer is ending, which will be followed by an even longer winter, sometimes lasting years. The King’s Hand, a trusted advisor, has been murdered. He summons his old friend Eddard Stark to fill the post, pulling him into political conspiracies still alive among the ruling families. Meanwhile, the children of mad Aerys are still alive and planning their return to the Seven Kingdoms. Additionally, there is an unknown evil force growing up beyond the Great Wall on the northern border.
A Game of Thrones (A Song of Ice and Fire, Book 1)
A Clash of Kings (A Song of Fire and Ice, Book 2)
A Storm of Swords (A Song of Ice and Fire, Book 3)

The Chronicles of Narnia by CS Lewis
The seven book Chronicles of Narnia are the only children’s books Lewis wrote. The Lion, the Witch, and the Wardrobe was one of the first fantasy novels I ever read, as I am sure it was for many. The newest printing places the books in the order CS Lewis thought they should be read, which is not the order in which they were written. In this new edition you can read from Aslan’s creation of Narnia all though to the final battle between good and evil. To learn more about each individual novel, or information about the future movie, visit Narnia.
The Chronicles of Narnia Boxed Set

Discworld by Terry Pratchett
The novels of Discworld are funny, intelligent and satirical. The world is a disc that moves through space on the backs of four elephants, which are on the back of a giant turtle. There are many novels based in this world. Though they are written to be independent, many center on the same characters. There are the Rincewind books, the Witches books, the Death books, the City Watch books, and others. These are two of my favorites:
Small Gods (Discworld Novels (Paperback)) Belief is a great power in Discworld. As a god gains more believers his power grows accordingly. Therefore “small gods” are ones with few or no true believers. The Church of the Great God Om is a fearsome religion, complete with inquisitions. One day while in his garden, novice Brutha hears a small voice that claims to be Om.
Carpe Jugulum (Discworld Novels (Paperback)) pokes fun at vampire literature. Count Magpyr and his family are invited to a christening in the mountain country of Lancre. When they decide not to return to Uberwald, the witches need to find a way to get them to leave.

The Sword of Truth by Terry Goodkind
I must admit, I have only read the first two books in this series (I believe there are eight now). I have tried to read the third, but I felt the characters seemed to have suddenly changed personality. That said, I thoroughly enjoyed the two I did read.

In Wizard’s First Rule, the world where Richard Cypher lives has no magic. When he meets a mysterious woman, Kahlan, his world begins to change. He finds himself out of his beloved Westland and in a land of magic, needing to learn to use his magical sword or face dire consequences. Stone of Tears continues the relationship between Richard and Kahlan. In order to save Richard’s life, Kahlan must send him away, committing the ultimate betrayal. Meanwhile she must stop a war from engulfing her world.
Wizard's First Rule (Sword of Truth, Book 1)
Stone of Tears (Sword of Truth, Book 2)

There are many other good series out there, but these are the few I have personally read. Some that I have heard good things about (but haven’t read) are:

Robert Jordan’s Wheel of Time, now in three box sets
The Wheel of Time (Boxed Set #1)
The Wheel of Time (Boxed Set #2)
The Wheel of Time (Boxed Set #3)

Be sure to look for more recommended reading in the future!