Since the current crop of Kindles have been out for a while, there's now a large selection of accessories. This is the first in a series of posts on current accessories that are useful when travelling with your Kindle. I'll focus on the Fire, Touch, and plain Kindle (which I'll call the Basic).
One important trick- when searching Amazon for Kindle accessories, don't just search in the Kindle Store. The items there are "official" Kindle accessories- but there are many more in other departments, such as electronics, that are usually cheaper and often just as functional.
The most important item to have is a protective cover or sleeve. I prefer a cover so that I don't have to remove the Kindle to use it, and also I like the grip I get with a cover. If you prefer to use your Kindle bare then you may prefer a sleeve. Sleeves also have the advantage of working with other devices of about the same size.
For the Kindle Fire, I like the Kindle Fire Lightweight MicroShell Folio Cover by Marware. It's a bit pricey but very light while still being protective. The cover also folds back so you can prop the Fire up at a 45-degree angle in landscape mode for watching movies, etc. A much cheaper alternative is the Poetic 360 degree Rotary leather case. Although a bit heavier and bulkier than the Marware case, the Poetic case lets you prop up the Fire in either portrait or landscape orientation.
Because of the Fire's weight you may prefer to use it bare. In that case, the Timbuk2 Kindle Fire Plush Sleeve is a popular way to go. Another good sleeve is the SumacLife Neoprene Sleeve Carrying Case Cover. This case has a pouch for accessories such as earphones.
If you use the Fire bare or even if you have a case that props the Fire up, you may find a stand useful. Stands have the advantages of working with more than one device, so if you own a Touch and a Fire as I do, you can use it with both. Stands also let you prop a Kindle in either landscape and portrait positions at variety of angles. The Arkon Portable Fold-Up Stand works with everything from the smallest Kindles to a 10-inch tablet.