My 3 and 6 year olds each have one of my discarded Asus eee-pcs, used mainly for web and open office.
As far as the web's concerned, their homepages are set to CBeebies with a few other favourite sites bookmarked, and these are all they go to. They don't have email or chat, and I (gasp) haven't introduced them to the concept of search, so their chances of finding something undesirable are pretty limited, at least for now.