Having a website on WordPress platform requires us to have a web server to host our WordPress installation, though there are plenty of free and cheap offerings for WordPress web hosting, but they aren’t worth the trouble, and getting a good plan like dedicated server hosting means spending huge bucks.
One of the top notch web hosting service provided is Amazon EC2, having a website there gives us plenty of advantages like scalability(means we can scale up/down dynamically with no downtime), no server maintenance(as they will do it), easy upgrades of softwares(like php, MySQL) and plenty more. However, Amazon EC2 is not a “free web hosting” provider(although there is a Free Tier, but it is limited) but still we can get our website up there for no cost using OpenShift.
Openshift is a PaaS offering, which is meant for users and developers to share code/applications with community. That is, it is not exactly a web host, but you can host a WordPress installation in it as well. It also means that the PaaS provider will take care of all the security updates(and all that we get with regular Amazon EC2).
I am not going in details of how you can set up a WordPress installation on an OpenShift account since Amith Shah has already done this, check the blog post at http://log.amitshah.net/2011/12/blog-moved-to-wordpress-on-openshift/.