From office desktop: RDP to our jumpbox (remote access to all clients), VNC to customer gateway server, Terminal Services to internal network jumpbox, TS to server I need to work on.
It is agonizingly slow, and VNC never updates the screen often enough.
Give yourself 100Mb (or better, 1Gb) dedicated links between each system, and quad-processors of the fastest models available and plenty of memory, and it'd probably be pretty usable even through several systems. But you still end up with a window within a window within a window within a window, and they all have scroll bars which take up more and more space relative to the usable desktop space. Unless you use full screen mode for each connection, which is fine if you only care about the final node and don't need to switch back to any previous nodes.