You can find cool backgrounds just by using your basic search engine. Now it is easy to even search the images part of the search engine to make this a painless task. If you are looking for some sort of pink and black Victorian design for example, that is what you will type into the search box. "Pink black Victorian" is what you will put in the box and see what comes out of it. If it is paisley you prefer, then type in the word "paisley" and search images.
If that is not for you, you could then search for websites that have cool backgrounds that are up for grabs. Many of these websites organize the backgrounds based on color, design, and how large the monitor or screen is. When looking for obscure cool backgrounds, such as the ones dedicated to favorite bands or television shows then checking the fan sites devoted to them might prove to be more than fruitful. These amateur artists tend to be genius at designing beautiful cook backgrounds and even are known to add favorite quotes which adds to its personality.