While I was looking for a remote desktop client solution for Linux, I was directed to Teamviewer 9 by a friendly person on the #ubuntu channel at irc.freenode.org.
While I couldn't get the 64 bit version to work for my Ubuntu 13.10 64 bit install, the 32 bit "multiarch" version worked just fine for me.
I love this client. Their are other remote desktop clients available, with many available functions.
But when it comes down to ease of use and simplicity, Teamviewer shines like a halogen flashlight in a railway tunnel.
You are seeing the main control of Teamviewer. If you want someone to connect to you, then you give them the information on the left side of the window.
If you want to connect to someone, you feed the information they gave you from their Teamviewer's left side into your right side.
Once you punch in the password (if you are the one connecting), You will see a window showing their desktop.
It looks like this:
Clients like Remmina have more options, but the simplicity and ease of use of Teamviewer has won me over.
Is Teamviewer the easiest remote desktop client? I believe so.
Make up your own mind!
Here's where you can get it for Linux:
For other operating system options, check this site out: