Here's a short list of 32 book's I've read that really affected how I look at the world (with links to Goodreads):
0) The Dancers at the End of Time Trilogy by Michael Moorcock - A literary dandy of a series. Short, sweet, funny and eternally optimistic. Stays with you.
1) The Illuminatus! Trilogy By Robert Shae and Robert Anton Wilson. - Truly hilarious - the literary equivalent of taking LSD. Once you've read it you'll never see the world in the same way again. This book invented the Illuminati conspiracy myth as we know it today.
2, 3, 4, 5) Hyperion / The Fall of Hyperion / Endymion, The Rise of Endymion by Dan Simmons - Heavy, difficult, big-idea science fiction / space opera set in a deeply religious future. The end made me cry. (Also check out Drood by Simmons. It's creepy and great.)
6) Solaris by Stanislaw Lem - a moving and beautiful critique of the scientific process - also made me cry. (read any Lem you come across, it's all great)
7) Gravity's Rainbow by Thomas Pynchon- a monster of a book - took me 3 years to read - but worth every bit of it. Affects how you perceive the world. (Also worth reading the companion so you can see what you missed the first time around)
8) Accelerando by Charles Stross - Truly a book for our times. Read any Stross, it's all pretty good.
9) The Master and Margarita by Mikhail Bulgakov - funny, trippy satire of the soviet era and religion.
10) The Sacred Book of the Werewolf - Funny, especially if you've read The Master and Margarita by Bulgakov but ultimately this is a book about the nature of perception and reality.
11, 12, 13) American Tabloid / The Cold Six Thousand / Blood's a Rover - James Ellroy. - Shocking, funny, tense, amazing. You'll never look at US politics in the same way again. Very few sentences longer than about 4 sentences unless it's dialogue, newspaper extracts or wiretap transcripts.
14, 15, 16) The Baroque Cycle by Neil Stephenson - Terrific fun nerd core historical adventure that reveals the history of money and science. Then go read all of Stephenson's other books, especially Cryptonomicon, Snow Crash, The Diamond Age and Anathem.
17) The Gulag Archipelago by Aleksandr Solzhenitsyn - scary because it's true and increasingly relevant. You'll look twice at train carriages after reading this.
18) Any / all of the Culture books by Iain M Banks, but especially Surface Detail.
19 and 20) The Commonwealth Saga by Peter F Hamilton - pure fun space opera.
21) The Hitchhikers Guide to the Galaxy by Douglas Adams. Should be mandatory reading for everyone.
22 and 23) Animal Farm and 1984 by George Orwell - Also should be required reading.
24) Slaughterhouse Five by Kurt Vonnegut Jr. And indeed any KVjr
25) Cloud Atlas by David Mitchell - funny, clever, trippy and interestingly structured.
26, 27, and 28) The Road, No Country for Old Men, and Blood Meridian by Cormac McCarthy - bleak and terrifying each in their own way. Amazing writing.
29) Flood and Evolution by Stephen Baxter - post apocalyptic funtimes.
30) World war Z: An Oral History of the Zombie War by Max Barry - best zombie book ever.
31) Bitter Seeds by Ian Tregillis - Demons vs Ubermench during WW][. Scary and weird but creepy good fun.
I could go on but if you get through all of these you'll never look at the world in the same way again.