I set all of my family members up with Linux Mint so that their computers would stop punching themselves in the face, but I'd like to be able to control those computers when my mom calls up and wants to know how to "put her favorites in the drop box." I've got Parallels with WinXP, and Ubunutu VMs, so my OS isn't really a concern (although I'd prefer to use OS X if there was a slick GUI app). What's the best or most practical approach to getting access to these computers from across the country?
Definitely SSH. You could set up an under-privileged account with
sudo-level privileges and connect to the box using that account over SSH to administrate the box. And, if you are looking for a graphical alternative, there is of course VNC: by setting up a VNC server on the remote box, and using the Chicken VNC client on OS X, you could have a graphical remote access to the box.
NoMachine's NX Free Edition can be installed on Linux hosts, and they have NX Client versions for Windows, Mac, and Linux.
You could use a VNC server and client (see here for more: http://www.skullbox.net/vncserver.php). Essentially VNC is what Remode Desktop is on Windows, i.e. allowing one computer over a network (or internet) to access a 'screen' on another computer. There are VNC servers and clients available for Linux and MacOS (you'd need a server on the Linux and a VNC client on the Mac).
NoMachine is available for mac, linux and windows clients as well as servers at http://www.nomachine.com
you can use x2go its graphical and uses x forwarding over ssh over tcp. Easy to install the server in linux. on mac side just take the apropriate client