Only the Kindle Fire is backlit. The rest of the Kindle family are not lit. Among the many lights you can buy to use with a Kindle, some are able to plug directly into the Kindle, thereby using minimal power from the Kindle and do not need battery replacement.

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The reason the Kindle only has to be recharged every couple of weeks is that it uses a technology called e-ink (which is sort of like a high-tech etch-a-sketch), and this technology does not rely on backlighting. If you had a reader with backlighting or a built-in light, you would be charging it quite frequently. The only downside is that you can't read in bed in the dark. However, there are many nice, small reading lights you can get to clip on, and there are some protective cases that also include a slide out lamp.

Depending upon which type of Kindle you have, Amazon sells covers with built-in lights. I have the Kindle with a keyboard below the screen & have a hot pink cover with a built-in light, & I love it.

Here is a link that might be useful: Kindle covers

My sister uses the cover with built-in light, says she likes it.

Reading on a backlit screen is harder on your eyes. You will notice eye strain/fatigue more from a backlit screen than a screen like the Kindle where you shine light onto the screen.

The Kindle Fire is backlit, but its primary purpose is not for reading e-books.

The Kindle covers that have the built-in lights draw the power from the Kindle, as Donna Loomis said, so they will cause the Kindle battery to run down more quickly if you read a lot using the light.