Techinline's Remote Desktop

Source
There are various remote assistance software  but it must be mentioned this too:
Techinline’s Remote Desktop in-browser tool which lets you set up a remote desktop session right from your browser through a browser plugin. No need to install any additional software.
3 Easy Steps to Start a Techinline's Remote Desktop SessionStep 1 : Log into the Techinline Expert console at techinline.net/expert. (Create an account first)
Step 2 :  Tell your friend or client to go to FixMe.it, where he/she receives a 6-digit number (Client ID)
Step 3 : Enter the Client ID obtained by the remote client into the corresponding field (see below) and click Connect.

Note, from the other end the user must click Accept to confirm and hence initiate the remote desktop session.
Once you have connected to the Client as the Expert, you can do any of the following:

• Remotely view the Client’s desktop
• Remotely view the Client’s desktop and control the Client’s mouse and keyboard
• Remotely restart the Client’s computer
• Allow the Client to remotely view your desktop
• Allow the Client to remotely view your desktop and control your mouse and keyboard
• Transfer folders, files, and text
• Interact with the Client via built-in text chat

You can refer to their online help docs for more details and information on how to use the tool.

Though it’s not a free tool but I didn’t find any similar in-browser tool to set up a remote desktop connection with so much ease.
Google Chrome has a free official extension called Chrome Remote Desktop BETA for setting up remote desktop between chrome users who have installed that extension.