Here's another report on backlit tablet devices and how they disturb your sleep cycle. The Kindle does not cause the same problems, as it uses the reflective e-ink technology.
Update: I was reminded by a reader that the Kindle Fire is backlit, so that is a device you should NOT be using at bedtime. The less expensive black and white Kindles are the e-ink models and do not have a back light.
Yet Another Update: Amazon just released a new Kindle Paperwhite and Paperwhite3G....with higher screen resolution....and...a backlight! They even have a picture of someone reading in bed in the dark using the backlight. Somehow they forgot to mention "Warning: use of the backlight before bedtime will keep you up all night."