For example, a large majority of tech startups have a WordPress blog that is totally separate from their actual web application. In many cases it also drives the marketing front-end of their website.
So while my main application may be on Heroku or AWS, I like to fire up a free PHPFog (I don't work for them, you could use DotCloud, or likely another alternative as well) account, and have my WordPress install setup there. It's insanely easy to setup (it's all Git based), and the free account will get you a long way.
It's also nice to know that the WordPress install lives on an entirely different server, so if you get slammed with great press, your entire stack isn't feeling the heat. There are security fears here as well, so I like having it separate.