Amazon EC2 Now Has Static IP Addresses

Or as they like to call them, Elastic IP Addresses. It is actually a pretty interesting concept that allows you to get a static IP address assigned to your account which you can then point to any particular EC2 instance. So if you take a server down, you point the Elastic IP to a new instance and the outside world still uses the same IP. Here's Amazon's description:

Elastic IP addresses are static IP addresses designed for dynamic cloud computing. An Elastic IP address is associated with your account not a particular instance, and you control that address until you choose to explicitly release it. Unlike traditional static IP addresses, however, Elastic IP addresses allow you to mask instance or Availability Zone failures by programmatically remapping your public IP addresses to any instance in your account. Rather than waiting on a data technician to reconfigure or replace your host, or waiting for DNS to propagate to all of your customers, Amazon EC2 enables you to engineer around problems with your instance or software by quickly remapping your Elastic IP address to a replacement instance.

Of course, you can still use dynamic dns (explained here) too.

Pricing:

No cost for Elastic IP addresses while in use
$0.01 per hour when not mapped to a running instance
100 free Elastic IP remaps per month per account and $.10 per remap thereafter