What are some alternatives?
When comparing BitBucket and OpenShift, you can also consider the following products
GitHub - Originally founded as a project to simplify sharing code, GitHub has grown into an application used by over a million people to store over two million code repositories, making GitHub the largest code host in the world.
Google App Engine - A powerful platform to build web and mobile apps that scale automatically.
GitLab - Create, review and deploy code together with GitLab open source git repo management software | GitLab
Heroku - Agile deployment platform for Ruby, Node.js, Clojure, Java, Python, and Scala. Setup takes only minutes and deploys are instant through git. Leave tedious server maintenance to Heroku and focus on your code.
SourceForge - SourceForge is a web-based source code repository.
Microsoft Azure - Windows Azure and SQL Azure enable you to build, host and scale applications in Microsoft datacenters.