With the advent of HTML5 (specifically WebSockets and the
element), it became possible to create browser based remote desktop clients that
run without requiring a browser plugin. With an HTML5 RDP client, you can open an
HTML5 compatible browser (Chrome, Firefox, Safari, or IE10), pull up the RDP client
page, and login. One click and you're remotely controlling the machine right from
the browser. No ActiveX, Java, or Flash plugins required.
If you want to check out clients for a different OS, go back to the Remote Desktop Clients index.
Unfortunately, none of the current HTML5 clients are standalone pages or components -- i.e. they can not run directly in your browser and connect to a raw RDP server. Instead, the HTML5 clients currently available require either server installation on each host machine to be accessed, or the installation of a gateway server.
There are several such servers listed in the HTML5 Remote Desktop Servers topic.