Long story abbreviated:
I have two children, 5 and 7 years old. The primary school would like them to have ready access to the school's VLE website. I happened to have two old laptops, both semi broken and under powered - but fine with a light OS and sitting on a table plugged into the wall. One laptop is a 6 year old HP, the other an Asus eeePC.
I decided on Xubuntu (Ubuntu but with the less hungry XFCE window manager), version 10.04, a Long Term Support release, maintained for 3 years.
Two base installations later, I then integrated the laptops with my home systems and locked the WIFI to my base station (ie removed NetworkManager).
Then a cursory configuration of each of their desktops - fix the fonts to be a bit bigger for small kids, clean up the "gnome style" twin task panels into a more Windows like single panel (the aim here is to allow them to feel comfortable going between my systems and the school computers). Added some media players and Flash so that the school VLE website worked correctly and defaulted Firefox to the school VLE.
The last jobs included installing the ubuntu-edu-primary metapackage, which adds lots of great education stuff like a fractions quiz, hangman, kiddie friendly paint program and lots of other stuff. Added GoogleEarth too.
My daughter (7) had a chance to further customise her desktop with verbal guidance and I fixed my son's (5) up by asking him what background colour he'd like.
It is quick and responsive, uncluttered and has a rich environment perfect for kids their age. My daughter is even learning perl programming. They know about logging out, saving files, hibernating and remembering to turn the power off.
They have few problems with the differences between Linux and MS Windows - the "Start" menu is in the same place and does similar things. Most apps have a similar menu layout (eg "File/Save", "Edit", "Help" and the more common keystrokes such as CTRL-C/V/X copy/paste/cut and CTRL-S save are the same anyway.
So overall this has proven a great success. Total cost of legitimate software: £0