http://aws.amazon.com/simpledb/
SimpleDB is a non-relational store that automatically indexes everything, but can only store up to 10GB. It's very flexible but limited, good for prototyping.
http://aws.amazon.com/dynamodb/
DynamoDB is like SimpleDB's grown-up version. At greater cost and with more up-front configuration, it scales automatically to huge workloads. It's still a non-relational store, with the drawbacks that implies.
Relational Database Service is literally managed MySQL instances. Amazon spins them up for you, manages configuration, backups and restoration. One of RDS's primary value-adds is that it can automatically partition your data across multiple EBS volumes (like hard drives). This helps get around the relatively low I/O performance of EBS volumes.
So pick your poison -- if you don't need high performance, simpleDB or a small RDS instance will work; it depends whether you want relational data or not. I can't speak for the difficulty of migrating; we stuck with running our own MySQL instances from the start.
For a lot of reasons (that I can enumerate if you'd like), we think running your own DBs is the best option.