It really depends on the applications. WordPress, Drupal, etc. have built-in mechanisms for handling application upgrades and we configure them so it works out

It really depends on the applications. WordPress, Drupal, etc. have built-in mechanisms for handling application upgrades and we configure them so it works out of the box. We have "native stack" deployments that hook up to the underlying Apache, MySQL, etc. so you can use the existing native package management tool for upgrading and patching your stack (the drawback is that support is restricted to the server versions supported by the OS). Finally, the most popular method, and what the Cloud makes really easy is to do: just spin up the new version of the app and move over the data. If everything goes well, just shutdown the old machine and use the new one.