It's not very open-source/Linux but the best remote desktop I've found so far for the Pi is the venerable Windows RDP (Citrix Winframe or whatever else you want to call it). I know you should be able to run an X-server and all would be well but I haven't been able to find a nice combo that works across all my Windows, Mac and Linux boxes; RDP is the only lingua franca.
So - to set it up on the Pi;
- Start up your Pi to the terminal prompt.
- Type the following command "sudo apt-get install xrdp"
- If promoted enter your password (the default is "raspberry")
- Type "Y" and press enter.
- This is now installing xrdp onto your Pi which is the software we are going to use for the remote desktop connection. Wait for it to complete.
- Restart your Pi. We are going to check that xrdp is going to start up automatically.
- When your Pi has booted to the command prompt look for [ ok ] Starting Remote Desktop Protocol server : xrdp sesman. This shows you that xrdp is installed and automatically starting up on start up of your Pi
It takes best part of half an hour to extract and install but once running it's the most responsive experience - far better than VNC and even better than Apple remote desktop. Not quite as good as sitting at the machine (or over an Amulet/Teradici network connection) but excellent none the less.
If you want to get to it via your router or firewall open one port - TCP; 3389.
Client for OS-X, Client for most Linux versions.
An alternative guide from May 2016;