While designing a new deployment system for my company with Amazon's AWS, I stumbled onto a problem that cost me some time - I could not get my EC2 instances to connect to our Amazon RDS database servers. I figured I'd document the solution here for the sake of those to follow.
I had created two webservers, and a MultiAZ instance of an RDS server with which they were to transact. I could connect to each webserver and the RDS server directly, but I could not get the webservers to connect to the RDS. The issue ultimately ended up being related to my security groups configuration.