As makeuseof.com said:
For Windows, built in remote desktop works great but you need a client to connect, and if you use a VNC (RealVNC, UltraVNC, etc) you also need a client – either standalone or a java-based one built into a webpage. Every remote desktop application I’ve seen requires some sort of browser plugin – until now.
ThinVNC takes remote desktop to a whole other level. The “VNC” part of its name is a huge misnomer – it does not use the VNC protocol at all. What they have done is written their own remote desktop software from scratch that implements HTML5 as a front end – meaning that any web browser that supports HTML version 5, such as Chrome, IE, and Firefox; can display and interact with the remote computer.
ThinVNC has free and paid solutions for web remote access.
There's also a ThinRDP solution.