I've talked on the blog and elsewhere many times about the importance of reading if you plan to become a good writer. I'm sure you can write without reading - well, knowing how to read seems to be a requirement, but reading other works is technically optional. Stephanie Souders wrote a wonderful essay about this recently. I recommend you read all of it, but here's the kernel:
"And if you are an author? Reading the classics will acquaint you with the genre’s norms. You have to read the Big Conversations before you add your two cents. You have to learn the rules before you seek to stretch or break them. Attempting to write science fiction without striving to be minimally familiar with the fundamentals is like trying to write a persuasive essay without learning how to write a grammatically correct sentence. It doesn’t work, and it leads to pseudo-science-fictional tripe."
Read broadly, or you run the risk of becoming narrow-minded. And it will, I promise you as a reader, show in your writing.
It's not hard to discover the classics. Many of the older ones, long out of print and copyright, are being reborn into ebook form, and often are free to download. And for those who prefer paper, or a title you cannot locate online, there are the penny books. It's becoming a big business, this rescuing of books from landfills (or at least on their way to one) and selling them on Amazon for a penny.
Some of my favorites, from the free books online, these are titles I read and loved long ago, which influenced me as I turned to writing. There are others, but this list is for those who can't afford to buy all the books!
Princess of Mars by ER Burroughs
The Strange Case of Dr. Jekyll and Mr. Hyde by Robert Louis Stevenson
The Time Machine by HG Wells
The Lost World by A Conan Doyle
Star Soldiers by Andre Norton
Deathworld by Harry Harrison (actually, I read the Stainless Steel Rat books avidly, but they aren't free... although I highly recommend them)
Lion Loose by James Schmitz (I love the Telzey and Trigger stories, which you can find here but not free).
On Basilisk Station by David Weber (what, they don't have to all be old!)
A Hymn Before Battle (again, not old but well worth reading) by John Ringo
Redliners by David Drake
The Insidious Dr Fu Manchu by Sax Rohmer
She by H Rider Haggard
Cobra by Timothy Zahn
Anything you can do... Randall Garrett
At the Back of the North Wind by George MacDonald (classic in fantasy and I loved all of his goblin books, too).
I could sit here and do this all night, but I'm sure you have your own favorites, and this is a good jumping-off point for my readers, who are likely familiar with these... but maybe not all. So hopefully I've sparked you into thinking about your favorite classics, share in the comments!