As with many other things in modern life, nothing is as simple as it initially seems...
Firstly, here's a quote from your service agreement that you checked off when you initially bought the device:
"Unless specifically indicated otherwise, you may not sell, rent, lease, distribute, broadcast, sublicense, or otherwise assign any rights to the Digital Content or any portion of it to any third party, and you may not remove or modify any proprietary notices or labels on the Digital Content."
and from "Selling Your Kindle" on Amazon's support page:
"You do need to remove all purchased material from the Kindle device. Purchased Kindle content cannot be sold according to the License Agreement and Terms of Use of the Amazon Kindle."
As most of us couldn't give a whit about violating Amazon's License Agreement, it may well come into play if you buy a new one and want to transfer the account you currently have with Amazon to your new device.
Problem is, giving away the device doesn't do the reciever much good unless they set up their own account with Amazon (who, by the way, is in the business of selling books not Kindles) in order to download books. Additionally, you may have credit card or other information on the Kindle as it currently exists.
At the very least you need to erase anything on the Kindle you're giving away. To do so, you need to take it back to the "Factory Reset" by restarting it (from the Settings menu) and holding down the Home key while it is rebooting. You will then be prompted as to whether you want to do a factory reset, which you deffinitely do...