Here are links to some web pages of authors that I either like or at least think are interesting. I'm also including my own descriptions of the authors and which of their books I particularly liked. Children's book authors are listed at the bottom of the page.

Douglas Adams
I found his Hitch Hiker's Guide to the Galaxy series quite funny, but it doesn't appeal to everyone. It's humor with a science fiction background. A lot of the humor is in how bizarre and random it is. The earlier books are better than the later ones. If you like them, you should also try Dirk Gently's Holistic Detective Agency which is funny in a similar but totally different way.
Issac Asimov
Asimov wrote a huge collection of science fiction, of which I've only read a small number, including his Robot series and some of his short stories. I would say that he is one of the "classic" science fiction writers. He also has a large number of non-fiction science books in mathematics, astronomy, physics, and other areas which range widely across different levels of detail.
Jane Austen
Pride and Prejudice is one of my top favorite books, and Jane Austen is one of my top favorite authors. Her novels are about upper class British social life, particular the lives of young single women and their families, and are filled with sarcasm and dry humor. Other favorites by her are Emma and Persuasion. If you like her, try the Bronte sisters.
Anne Bronte
Of the three Bronte sisters, Anne's novels are probably the least well known, but I like them as much as those of her sisters. Both Agnes Grey and The Tenant of Wildfell Hall are worth reading.
Charlotte Bronte
Charlotte is probably the best known of the Bronte sisters as the author of Jane Eyre, a wonderful book that I recommend to anyone. All three of her novels (the others being Shirley and Villette) are about the lives of young single women trying to fend for themselves in a proper British world. If you enjoy these books, you should also try her sisters.
A.S. Byatt
Byatt is probably my favorite author, with her novel Possession being possibly my favorite book. However, I have yet to read anything by her that I did not love. Her books often have themes of literary criticism of other authors (real or imagined) woven into them. She draws from fairy tales and folk stories but views them with a modern eye. If you have tried Possession and had a hard time getting past all of the poetry or would like to start with something less complicated, I would recommend her two novellas Angels and Insects or The Djinn in the Nightingale's Eye : Five Fairy Stories.
Lewis Carroll
Lewis Carroll (real name Charles Dodgson) is the author of Alice's Adventures in Wonderland and Through the Looking-Glass and What Alice Found There. Both are fun and sometimes silly books featuring wonderful twists of logic. Which makes sense, since Carroll was also a mathematician and wrote some interesting books about logic as well.
Arthur C. Clarke
Another "classic" science fiction author - some of my favorites by Clarke are Rendezvous with Rama and its sequel Rama II (written with Gentry Lee) and The Songs of Distant Earth. He also wrote 2001: A Space Odyssey and its sequels.
Michael Crichton
If you've seen a movie version of a Crichton novel all I can say is, the books were much better. The most interesting parts of his books, the bits that reflect on the world and our growing dependence on and trust in technology, don't translate well to movies, in my opinion. I loved The Terminal Man and Disclosure. The former looks at what happens when we take the analogy between the human brain and a computer too far and the later is a look at sexual harassment against the backdrop of the computer industry. Jurassic Park was a good book to which the movie was not very faithful. I also enjoyed The Andromeda Strain, Sphere, Rising Sun and A Case of Need (written as Jeffrey Hudson).
Simone de Beauvoir
This French feminist was the author of The Second Sex, a classic feminist work.
Charles Dickens
While some people find Dickens dry and boring, I've enjoyed some of his books. My favorites are A Tale of Two Cities (his best book that I have read so far), Dombey and Son and Great Expectations. If your judgement of Dickens is based on A Christmas Carol or Oliver Twist, I didn't like these that much either, so you might want to give him another try.
Emily Dickinson
Emily Dickinson is an American poet who wrote during the mid-1800s. There are some nice collections of her work out there.
Fyodor Dostoevsky
Crime and Punishment was the first novel I read by a Russian author and I've re-reaed it several times since then. It's another favorite book of mine. I've also read and enjoyed The Brothers Karamazov. Both these books examine both Russian culture and human nature in general.
Daphne du Maurier
Du Maurier's novels float somewhere between the romance novel and literature genres. Her novel Rebecca is my favorite and was made into a movie by Hitchcock which was also quite good. I haven't enjoyed her other books quite as much, but they tend to be pleasant to read, if not overly deep.
Sir Arthur Conan Doyle
Though Doyle has written other books, I've only read the novels and short stories from the Sherlock Holmes series. I don't really like mystery stories, but I make an exception for these.
George Eliot
I have a hard time describing George Eliot's books; if you don't like either Dickens or the Brontees, you might not like Eliot (the inverse is also true). I liked The Mill on the Floss.
William Faulkner
Faulkner writes in a stream of consciousness style which includes many paragraph long sentences. His goal is not to make things easy on the reader, However, the effort is worthwhile. He writes mostly about a Southern county that he creates the history and people of through the course of his books. My favorites are Light in August and the more difficult The Sound and the Fury.
Nathaniel Hawthorne
I wrote my high school English thesis on Hawthorne and love his novels but don't enjoy his short stories as much. The Scarlett Letter and The House of the Seven Gables are the best place to start. The former has more plot while the later is more introspective.
Douglas Hofstadter
Hofstadter writes non-fiction about science and technology, particularly those parts of it that relate to mathematics. He is the author of Godel, Escher, Bach: An Eternal Golden Braid. This book is about self-reference and recursion as it appears in art, music and mathematics and computer science.
Ursula LeGuin
A sceince fiction writer, I've only read her The Left Hand of Darkness but enjoyed it. In this one book I've read she plays around with gender roles, which I enjoy.
Stanislaw Lem
Another science fiction writer, Lem as a very weird streak. I don't understand a lot of what he writes but it isn't too long and the bizarreness can be fun. I suggest Tales of Pirx the Pilot, a set of short stories about a spaceship pilot which has some good twists and Memoirs Found in a Bathtub which is much stranger and seems to have a deeper meaning to it.
Anne Rice
Not a very deep writer, but Rice has writen some fun books. I thought that her Vampire Chronicles series was neat, though the later books aren't nearly as good. My favorite by her is The Witching Hour which follows a family through 13 generations of women who carry on a family tradition of being witches, not in the black hat and magic sense, but in the being able to communicate with spirits sense.
William Shakespeare
What is there to say - I like his plays. The language is a bit of a hurdle for the first few scenes until you get into it. My favorites are King Lear and Macbeth. If you ever get a chance to see Shakespeare performed on stage, it's definitely worth it.
J.R.R. Tolkien
If you ever read fantasy, you have to read Tolkein. The Lord of the Rings trilogy is so widely copied it's hard to find any modern fantasy that doesn't borrow something from it. The writing is just amazing. If you're looking for a gentle start, The Hobbit is a childrens story that preceeds The Lord of the Rings, though it is a full length book that I still love as an adult, and I think that it lends a lot to the trilogy to have read this book first. I wouldn't recommend picking up something else by him, such as The Silmarillion until you've read these other books, though once I got into Tolkiens world I enjoyed this book as well.
Evelyn Waugh
From what I've read, Waugh's books seem to be heavy in character development and the plot is used to also comment on social phenomenon and interpersonal relationships. I liked Brideshead Revisted which was in some ways a typical British novel of the time.
Viginia Woolf
I've liked Woolf's fiction as well as her non-fiction. Both are what I would consider feminist. A Room of One's Own certainly is, and I think that it is a valuable book for any woman feeling like her life is out of balance to read. Her fiction is often written stream of consciousness style and she likes to experiment with using different types of writing to reflect the themes in her book. To the Lighthouse is probably the best example of this type of thing. I also liked Mrs. Dalloway, which reminded me a little of Chopin's The Awakening.

Children's Authors

Louisa May Alcott
Little Women is her best known book, but I prefer Little Men, Eight Cousins and Rose in Bloom.
Hans Christian Andersen
These old fairy tales very different from our modern versions.
Judy Blume
Superfudge, Are You There God? It's Me, Margaret and Starring Sally J. Freedman As Herself are my favorites, but I recommend any of them.
Sigmund Brouwer
I've never read any of his books, by my sister and mother like him a lot.
Eric Carle
His illustrations are a lot of fun. Try The Very Hungry Caterpillar.
Beverly Cleary
I think her books about Ramona, Beezus and Henry are the most fun.
Roald Dahl
Charlie and the Chocolate Factory is great; what could be better than a candy factory that more closely resembles a kid's fantasy play castle?
Dr. Seuss
I like all his books, but my favorites are Cat in the Hat, Fox in Socks, Horton Hears a Who, and How the Grinch Stole Christmas.
C.S. Lewis
His Chronicles of Narnia are great, though I disapprove of the way that they have been reordered recently (Lewis said that he thought the new ordering was fine, though also commented that they could be read in any order at all). I suggest that you read them in the original order: The Lion, the Witch and the Wardrobe, Prince Caspian, The Voyage of the Dawn Treader, The Silver Chair, The Horse and His Boy, The Magicians Nephew and finally The Last Battle.
A.A. Milne
Milne is best known for his Winnie the Pooh books, which I think are best if you can get non-Disney versions.
Lucy Maud Montgomery
Anne of Green Gables and the rest of that series is good, but I liked her Emily of New Moon trilogy even more.
Maurice Sendak
Where the Wild Things Are is my favorite children's book of all. If you haven't read it, you are missing out.
Shel Silverstein
I enjoy his two poety collections, Where the Sidewalk Ends and A Light in the Attic; the poems range from thoughtful to bizarre to the downright gross, with the empahsis being on the bizarre.
Laura Ingalls Wilder
I read all of the Little House on the Prairie books multiple times, but Farmer Boy was my favorite, followed by Little Town on the Town.