The Kindle's default screensaver is (mostly) a wonderful selection of timeless authors. If you want something a bit more contemporary, or just want to make your Kindle a bit more you, it's possible to change your screensaver, provided you're willing to jailbreak your device.
Kindle Wallpapers is a simple Tumblog full of alternative wallpapers/ screensavers for your Kindle. Every image uploaded is 800x600 pixels, and, according to the site owner, most are small enough to come in at less than 100kb.
To apply a screensaver, you'll have to jailbreak your device, which comes with a few disclaimers. If you're undaunted, let the jailbreaking begin by following these instructions. Note that jailbreaking comes with more advantages than just screensavers: you can also customize your Kindle in other ways, like applying new fonts.
Now you just need to find a new image to use. The selection on Kindle Wallpapers is pretty extensive and eclectic, so you shouldn't have any trouble finding something that suits you. Here are a couple of examples:
If you have any issues with jailbreaking or applying the new screensavers, check out the previously mentioned instructions page (including the comments section) for help.
Few things are more personal than reading, so it can be argued that, since the Kindle holds most or all of your reading material, it should better reflect you and your tastes. Screensavers go a long way in accomplishing that task, and Kindle Wallpapers ensures that there's a screensaver available for nearly every taste.
Bonus: if you want to take the screensaver concept further, you can turn your Kindle into a full-fledged mini weather station.