Web hosting now has a Console tab. It opens a shell in your browser, the same one you get over SSH, without an SSH client or a password.
The console runs as your hosting's own user and starts in its home folder.
php, mysql and git are installed, so a quick git pull or a PHP script
no longer needs an SSH client.
The tab is available on every tier that includes SSH, to members who can make changes to the project. The session ends when you leave the tab.
See Web Hosting for more.