One of the worst things is if machine won't boot (happened once due to hard drive failing). Otherwise it uses a few dynamic dns sites so I can know its IP ( + a few links to the show me the IP links in her browser toolbar, just in case).
If there is a problem and need to help her with the desktop, there is x11vnc.
Disallow password login, use key-based auth (using a dedicated, passphrase-protected key that you can copy around).
An alternative is to have a "shortcut" that help them fire a SSH client connecting to a server of yours, with port forwarding allowing you to connect back, so you don't have to worry about firewalls and other appliances being reset.
So for example, my mom would say "I am not sure where to find the pictures". I would move the folder to her Desktop from ssh, hoping the would see it. But if not I ssh in, then launch x11vnc then connect to it with a vncclient and then move around her desktop to see what the problem might be.
She would see the mouse move and buttons getting clicked.
Bandwidth is not a problem because, we have have something like 50Mpbs connections, latency is usually the issue as the signal has to go half way around the world.
Still not perfect, but better.