What are some alternatives to upgrading without using the standard upgrade system? Suppose for example that I wanted to upgrade an Ubuntu installation on a machine with a poor Internet connection. What would my options be? Could I just use a standard Ubuntu disk to upgrade this machine? If I already have a standard Ubuntu disk and want to use that, could I do a clean install without wiping data?
You can use the alternative CD (instead of Ubuntu Desktop, Kubuntu Desktop, Server CD) which allows you to upgrade from CD.
You can do an installation of a newer version of Ubuntu over top of an existing installation. You'll lose all of your (non-local [1]) system files and applications, but it will preserve everything in /home.
Select the advanced partitioning option from the menu of either the desktop CD installer or the alternate CD installer. Set the mountpoint of your existing root partition to / and make sure the format box is not checked. Repeat these steps for your home partition, if you have one.
1: Where local system directories would be /usr/src, /usr/local, and /var/local