If you want a background image for your website (or even just your Twitter profile), a complex design won't cut it. Subtle Patterns is a handy collection of free background images that won't overwhelm your audience.
All the images are licensed as Creative Commons 3.0, so you can freely use them in your own work (it's always good manners to acknowledge the designer, even though that isn't technically a requirement). If you want to use them as wallpaper, there's a handy collection of images ready-rendered for wallpaper use too, as well as a PhotoShop pattern file containing all the designs. Thanks Phillip for the pointer!