Amazon allows for static IP's to allocated to its EC2 instances.
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 you have running. 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.
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 $0.10 per remap thereafter
Hope that helps.