Both my mum, dad, sister, girlfriend, mother in law, girlfriends granddad(!) are using Ubuntu now. This is what I did.
First let them use Firefox and Thunderbird (if they use POP/IMAP mail) and maybe OpenOffice.org for some time. This will give them a hands on experience with alternatives to MS software.
For most of the users the introduction to Firefox was a blast. They quickly noticed a much better web experience compared to Internet Explorer.
Then I offered them to try Ubuntu LTS. Installed it on a small partition on the disk, so they had dual boot. Then I told them to use Ubuntu for all their web surfing needs, etc. and only start up Windows, if they had to do something that would not work in Ubuntu. I also made them write down what didn't work, and we would look at it next time I visited.
Some of the users soon just stopped ever booting in to Windows.
So here is the status:
* mum: using Ubuntu LTS, but still has dual boot to Windows Vista because of a special application she needs at work.
* dad: only using Ubuntu LTS. I have had one support question about how to find imported pictures from a digital camera.
* sister: only using Ubuntu 9.10, but recently she needed a Windows application for school, so I installed Windows XP in VirtualBox. Apart from installing Win XP in Virtual Box, i have not had any support questions for over a year.
* girlfriend: only uses Ubuntu 9.10. I never have any support questions.
* mother in law: using Ubuntu LTS, I do not have any support questions. She primarily uses Firefox and OpenOffice. It Just Works for her.
* girlfriends granddad(!): Using Xubuntu LTS. Font size has been increased a bit from the default. I had one question about how to install a very old printer. Turns out the printer did not work on the computer (did not have parallel port), so he got a new printer.