You can now run an EC2 instance 24×7 for under $15/month with the announcement last night of the Micro instance type. The Micro includes 613 MB of RAM and can burst for short periods up to 2 EC2 Compute Units(One EC2 Compute Unit equals 1.0-1.2 GHz 2007 Opteron or 2007 Xeon processor). They are available in all EC2 supported regions and in 32 or 64 bit flavors.
The design point for Micro instances is to offer a small amount of consistent, always available CPU resources while supporting short bursts above this level. The instance type is well suited for lower throughput applications and web sites that consume significant compute cycles but only periodically.
Micro instances are available for Windows or Linux with Linux at $0.02/hour and windows at $0.03/hour. You can quickly start a Micro instance using the EC2 management console: EC2 Console.
The announcement: Announcing Micro Instances for Amazon EC2
More information: Amazon Elastic Compute Cloud (Amazon EC2)