Play Concentration with a deck of 52 playing cards. Match up pairs by memorizing the location of each card.
Buy a memory board game like Arthur or the Pooh Memory Game. These games are similar to concentration but they add a game board element. They also include characters that children like to watch on television and read about.
Find 5 fun items around the house. Put the items on a tray. Let the child view the items for a couple of minutes. Hide the tray and ask the child to tell you what items were on the tray. Add more items if 5 items is too easy.
Sing memory songs to really young children. Try the alphabet song or count by twos such as 2, 4, 6, or count by threes. Rote memorizing games help with multiplication facts.
Play computer memory games such as those at funbrain.com and zefrank.com.