Open Stack is open source software for cloud tooling avoiding competitors' vendor lock-in. Rackspace and NASA are the founders of this project.
Rackspace was initially a traditional hosting company. They transformed by providing customers with their own cloud services, powered by Open Stack. But they are also known for their managed cross-vendor cloud services.
Google App Engine is the original cloud vision by Google, where developers can host their app in the cloud, and have it auto-scale behind the scenes.
Digitalocean is a cost effective and developer focused cloud hosting company. Digitalocean has build a custom solution centered around droplets.
Heroku offers cloud hosting for apps. It early on became the go-to platform for Rails apps.
AWS (Amazon Web Services) is the market leader in cloud hosting, with a wide variety of services.
Azure by Microsoft is quickly gaining traction, attributed to their enterprise sales, after a relative late entry to market.
Google Cloud Platform has matured strongly in the past years, and makes an almost equal competitor to AWS.