LEGO.com is the official website of the LEGO Group.
Amazon.com is a great place to find deals on LEGOs. Make sure you take advantage of the super saver shipping.
Bricklink.com is an invaluable resource. Its main focus is as a marketplace where people can buy and sell LEGOs. If you are looking for 50 of a specific part for something you are building, then this is your holy grail. The site also hosts an incredibly useful reference catalog that lists what parts are in what sets. Want to know how many 1×1 tan bricks are in the Grand Emporium? Here you go!
The Brothers Brick is one of my favorite sites that focuses on interesting and creative builds.
Eurobricks Forum is an excellent place to share creations, talk with other LEGO fans, and compare notes of different sets.
Brickshelf.com is an image gallery where you can browse thousands of LEGO creations and even post your own.