Stitch is run entirely on AWS. All of our transactional databases are run with Amazon RDS, and we rely on Amazon S3 for data persistence in various stages of our pipeline. Our product integrates with Amazon Redshift as a data destination, and we also use Redshift as an internal data warehouse (powered by Stitch, of course).
The majority of our services run on stateless Amazon EC2 instances that are managed by AWS OpsWorks. We recently introduced Kubernetes into our infrastructure to run the scheduled jobs that execute Singer code to extract data from various sources. Although we tend to be wary of shiny new toys, Kubernetes has proven to be a good fit for this problem, and its stability, strong community and helpful tooling have made it easy for us to incorporate into our operations.