Most travelers are able to keep their Kindles (and cell phones, music players, and the like) charged by using AC power in hotels. Even those on extended camping trips generally like to rent a room occasionally, which is what I do on photography trips. But for extended travel away from sources of AC power, you'll have to come up with another power source.
On extended camping trips, you can charge your Kindle from the 12 volt power in your vehicle, assuming you're driving between campsites. If you're not driving, or if you're in the wilderness for extended periods such as a backpacking trip or river trip, or in countries areas where AC power is unreliable or the wrong voltage for your wall charger, then solar chargers are about the only alternative.
I've done some tests on the current Kindle models (except for the DX, which I don't own) to determine their power drain during charging. It turns out all of the Kindles draw around 500 milliamps (mA) to charge at maximum rate. The Kindle basic and the Touch both need about 460 mA, the Keyboard about 550 mA, and the Fire 445 to 640 mA. If your charger supplies less power, then it will take longer to charge the Kindle. For example, powered USB 2.0 ports on desktop computers and USB 2.0 hubs supply 500 mA, but unpowered hubs and laptop USB ports may supply as little as 100 mA. The newer USB 3.0 standard requires that these ports supply 900 mA.
Solar chargers come in two basic types- those with internal rechargeable batteries and those without. The difference is that solar chargers with batteries can charge your Kindle during the night or cloudy weather when there is no sunlight. There are two drawbacks to solar chargers with batteries- first, there is a loss of power with the additional step of charging the solar charger's battery and then the Kindle's battery. Second, the solar charger's battery may not have enough capacity to fully charge the Kindle or to run it. Most of these devices can be charged from a USB cable as well as from the sun, so you can make sure it's fully charged before leaving home.
I have a Scosche SolBAT II Solar Powered Backup Battery and Charger that puts out 445 mA in full sunlight, enough to charge any of the current Kindles. But in my tests the internal battery can only charge the Fire about half way. Still, that may be enough to keep your Kindle going until you have full sunlight.
A couple of higher capacity chargers, the Soladec Hybrid Solar Power Charger and the XTG Solar Charger, have enough power to fully charge a Kindle, but of course they are more expensive and weigh more.
The sCharger-5 is a higher-power solar panel only, without an internal battery. But at 1000 mA output it has enough power to charge a couple of Kindles, cell phones, or other devices at the same time.
A unique charger, the Solar leather lighted cover for Kindle basic has a solar panel on the cover that charges a battery in the cover as well as the Kindle's battery. It also includes a flip-up reading light much like the one on the Amazon Kindle Lighted Leather Cover. The solar cover is currently available only for the Kindle basic but models for the other Kindles are under development, according to the company. It appears to work well but of course is dedicated to a specific model Kindle.