Guacamole allows you to access to your VNC server using just a browser, an HTML5 + JavaScript (AJAX) viewer for VNC, which makes use of a server-side proxy written in Java. The current version is almost as responsive as native VNC and should work in any browser supporting the HTML5 canvas tag.

Read more about Guacamole and its features in its official site.

Update: As Mariana says in the comments, another web based VNC alternative is ThinVNC, a pure HTML & AJAX Remote Desktop implementation.