If you don't want to buy your kids a brand new desktop, laptop or netbook and you don't want them to use yours, you can give them a “new” computer using old hardware and a small Linux distribution, like Puppy Linux.
Puppy Linux is a compact distribution that can run on a CD, DVD, or USB drive. However, you can also install it on a hard drive. The minimum requirements for the distribution is a Pentium 166MMX processor and128 MB of RAM. Whether you install it on the hard drive, or you run it from removable media, your children will have a usable computer for browsing the web, homework, or just playing games. Speaking of games, there's a nice suite of educational and gaming software created especially for children, called Gcompris. This site has the step by step directions for how to install the software on Puppy Linux.