The Barney website is a great resource for educational games (and it's free, which is always a nice bonus). These are simple flash games, but for this age group simpler is often better. The folks at PBS are always adding new games so this is a resource that will never get old. Games include:
Every Animal Talks: Kids hear an animal sound, and click on the matching animal.
Catch the Monkeys: Pass the mouse over a monkey to "catch" it (a kinder, gentler version of "Whack-a-mole").
Jungle Friends Music Jam: Children can make music by clicking on a beat and adding animal sounds.
Celebrating Around the World: Mini-games designed to teach kids about the cultures and holidays of India, Ireland, Kenya, Brazil and Japan.
Older titles, such as Barney's Fun on Imagination Island and Barney on Location All Around Town, are unfortunately unavailable in stores, although they can still be obtained on auction sites such as Ebay. However, you might end up paying a hefty sum of $30 or more. Since the technology of these titles is very outdated, the free online games might be a better option.
However, Barney--Secret of the Rainbow is an excellent, inexpensive title for the PC. In this game, pre-schoolers must save the colors of the rainbow and return happiness to the land, by playing games focusing on skills like creativity, problem-solving, and memory skills. This title is lots of fun and has very good replay value.
The show itself is interactive in nature, and is full of games that parents can play with their children while watching it. These include dancing, singing, peek-a-boo, memory games and many others. The "Barney kids" also do various games and activities that can be easily duplicated by parents after the show. More than any of the other Barney products, the show itself is the best possible resource for games.