also you can browse this site, it has some great lists

goodreads.com

Oooh, also more re: classics, I've heard The Woman in White by Wilkie Collins is great (it's sort of mystery/suspense too, I gather. I haven't read it yet but it's been sitting on my bedside table for months. )

Also, have you read Agatha Christie? You might enjoy her books if you like Sherlock Holmes! (I've only read mostly her Poirot books, and they're great).

I recommend reading Still Alice by Lisa Genova.

Sci-Fi + classic = Ender's Game.

Fantasy:
- The most prominent "High Fantasy" book (other than lotr) I know is the "Wheel of Time" series by robert jordan. Warning though. It will take you a LONG time to get through this series. (12k pages)
-Another Mention to Brandon Sanderson and his Way Of Kings. Excellent potential.
-Terry Brooks is highly respected in the fantasy genre (Shannara series)
-Raymond E Feist writes a very entertaining novel. If you read any of his works start with "Magician". The books get better but thats the first one.

Another interesting read is A Dream of Eagles series by Jack Whyte. He tries to tell the story of King Arthur from a military based Historical perspective (its fiction). I found his work kind of refreshing from all the similar fantasy or love stories or action thrillers or any other book that essentially copies the style it originates from.

1984, crime and punishment, master and margarita, war and peace, anna karenina, anything by Dickens, Tolstoy, Dostoevsky, Chekhov (classics) (I'm a huge Russian lit fan so I'm a tad biased)
hopes and prospects, too big to fail, democracy incorporated, brain trust, emperor of maladies biography of cancer (non fiction)
LOTR, Chronicles of Narnia (fantasy)

If you're a Holmes fan read some of Doyle's stuff (the guy who created Sherlock).

Pillars of the Earth by Ken Follet!!!! I don't know anyone who has read it and didn't love it