A static website which just shows content can easily be achieved with the Nginx buildpack mentioned above, as well as a few other options. A more dynamic website that requires code running on the server (a web 'application') is an even better use case for Bluemix because you can write your server code (in almost any language) and run it on Bluemix (with essentially endless scaling) while taking advantage of many services that might help your application (want to store data..? use a data service. Want to send emails..? use an email service, etc. etc).
You can use nginx buildpack to setup static web site. To verify this feature, try this.
Create simple index.html file.
Push the file contents to Bluemix with nginx buildpack.