Really nothing is absolutely must have. If you carry your Kindle around often you will want a good sturdy cover or pouch to carry it in.
If you read at night in bed often, you will likely want some sort of lighting solution.
If you bought a Kindle 3 and the above two apply, I highly recommend the Amazon lighted cover. It is pricey but I've never found a better booklight and it is always right there. I have an Oberon cover for my Kindle 2 and it is beautiful but I'd still choose the lighted bookcover over it for function.
If you want to make your Kindle pretty there are a ton of skins and things but those are just decorative. The screen protectors are completely unnecessary. Don't waste your money there.
I bought the leather cover with booklight - worth every penny. Its "granny smith apple green" (that's what I call it) and cheers me up every time I see it.
I will also recommend the 59.99 cover that Amazon sells with the built-in light. I bought it after reading reviews on a lot of other covers, and am very pleased with my purchase. Mine is bright pink--- LOVE it. It is pricey, but WELL worth it for me!
I bought the leather cover with booklight - worth every penny. Its "granny smith apple green" (that's what I call it) and cheers me up every time I see it.
I have this too, in red. LOVE IT!!! The light is perfect--the other night I was stuck in the car waiting for my ds and pulled out my Kindle, flipped the light on, and was happy as a clam.