If your home computer has an always-on connection, just use remote control
software. For Windows, UltraVNC. For Linux, SSH + vncserver or FreeNX.
Something similar is sure to be available for free for Mac as well.

You'll probably have to mess with the firewall to get any of these going,
since there's a necessary inbound connection.

All of these have some kind of Java client, so as long as the computer you're
at has a working Java, you'll be able to connect. If you're using a laptop
while traveling, you can load a native client.