Kiddo has declared Skip-bo to be one of his favorite games. It uses strategic thinking but in order to win you need to keep your powers of observation well tuned.
Skip-bo is a classic card game for families.
Playing the game brings back a lot of memories for me. I first played it during a trip to my grandparents when I was a kid and have many fond memories of playing it over the years. Since the rules are a bit more involved than many other cards games for kids, it is best to follow the age guidelines of 7 and up, although no doubt there are many 5 and 6 year olds who could catch on quickly.
Bonus factoid: According to Wikipedia, Skip-bo is a version of Spite and Malice (what a name!), which you can play with any 52 card deck.
Other Games of the Month your kids will love: