If you are running databases on EC2, you will want to export the database backups using the native backup software for the database solution. Once this is done, you can synchronize the database changes over to an S3 bucket especially since they are very inexpensive to store. Doing this also means the data gets replicated across multiple regions, so if the database server needed to be brought up in another region or another availability zone, that would be done pretty quickly by synchronizing the data back from the S3 bucket.
It all depends on your needs, your risks, and how often your data changes. There's no one size fits all backup strategy.
First of all, stop procrastinating. Don't think you can get away without backups because things *will* fail.
Go with the most simple solution that fits your risk model. If you're okay with losing a days' worth of data in your application because things don't change very often, then maybe daily snapshots using the provider's snapshot technology is fine. If you need to have down to the millisecond backups, it's going to require a lot more time and planning to actually be able to handle that.