Is it possible to create a web based VNC/RDP-like client and server without use of plugins?

Assuming there is a publically available relay is there open source code available to create both a VNC/RDP-like client and server without using plugins/extensions or being browser specific? (e.g. no flash, no java, no active-x, etc). Or do all browser's security models void this scenario unless plugins are involved?

e.g.

1. user who has an issue navigates to url and starts a server instance within the browser

2. support rep navigates to same url but as client and then sees users computer.