I don't think this is true for DigitalOcean. I believe you have to destroy your VM ("droplet") in order to stop being charged. If it's just powered off, you're still billed for it. You can take a snapshot, destroy the droplet, and restore the snapshot later, but there is a small monthly charge for storing snapshot images as well.
"Am I charged while my Droplet is in a powered-off state?
Yes. Your diskspace, CPU, RAM, and IP address are all reserved while your Droplet is powered off. If you want to save a Droplet for future use take a snapshot of it and then destroy it. You'll be able to create a new Droplet from the snapshot image anytime to bring it back online."
