I'm a firm believer that if you're going to write or read modern fantasy/sci-fi, you should read as many of the classics as you can get your hands on. "Classic" is a very subjective term, so I'm going to limit my lists to some of my personal favorites. I'm also limiting the lists to novels published before 2000, because listing my current faves would take all night. (And I have Baskin-Robbins ice cream to eat, people.)
These lists DO NOT include all the fantasy & sci-fi novels I love. I'll add more in future posts.
* Some of the novels cross both genres, so I've randomly classified them in one category or the other.
** Books considered to be primarily adult novels are noted.
Classic Fantasy Novels & Series:
1) The Hobbit – J.R.R. Tolkein
2) Lord of the Rings – J.R.R. Tolkein
3) The Cronicles of Narnia – C.S. Lewis
4) Howl's Moving Castle – Diana Wynne Jones
5) A Wrinkle in Time – Madeline L'Engle
6) Frankenstein – Mary Shelley
7) Something Wicked This Way Comes – Ray Bradbury
8) The Dark is Rising – Susan Cooper
9) The Witching Hour – Anne Rice (Adult)
10) Interview With The Vampire – Anne Rice (Adult)
11) The Chronicles of Chrestomanci – Diana Wynne Jones
12) Dracula – Bram Stoker
13) The Last Unicorn- Peter S. Beagle
14) The Golden Compass – Philip Pullman
15) The Neverending Story – Michael Ende
16) Harry Potter – J.K. Rowling
Science Fiction Novels:
1) The White Mountains – John Christopher
2) Ender's Game – Orson Scott Card
3) Farenheit 451 – Ray Bradbury
4) The Giver – Lois Lowry
5) Dune – Frank Herbert
6) I Am Legend – Richard Matheson (Adult)
7) A Clockwork Orange – Anthony Burgess (Adult)
8) A Hitchhiker's Guide to the Galaxy – Douglas Adams
Author Holly Black (WHITE CAT, TITHE, THE SPIDERWICK CHRONICLES) also has an awesome list of fantasy reads on her website.

a #1 New York Times, USA Today, and international bestselling author and comic book writer. As an award-winning, Bram Stoker Award-nominated young adult author of 12 novels and graphic novels, she has been published in 51 countries and 38 languages and her books have sold more than 10 million copies worldwide. Kami’s best known works include the Beautiful Creatures series, Teen Titans: Raven, The X-Files: Agent of Chaos, The Lovely Reckless, Broken Beautiful Hearts, and the DC Black Label comic Joker/Harley: Criminal Sanity. She is also a cofounder of the Kid Lit book festival YALLFest.

Oh man, I have a lot of read to do >.< I love Howl's Moving Castle!