Baseball
Little League Baseball provides leagues for all ages. Players 7 to 12 are eligible for Minor League Division play, kids 9 through 12 can be assigned to Little League Division teams, and kids 12 to 14 can play in the Junior League Division. Local officials decide age cutoffs for each division. Girls are accepted as well. If there's no Little League in your community or if your kids aren't interested in competitive play, you can organize backyard Wiffle Ball games for kids in this age bracket.
Board Games
Board games are a classic way to spend a rainy afternoon. They span a wide range of age-appropriateness, so check the game's box to see whether they fit the 7-to-13 bracket. Classic games such as checkers, Chinese checkers, chess, and backgammon are solid choices. Classic board games such as Battleship, Twister and Trouble all work for kids 7 and older. Trivial Pursuit has a version for children 8 and older.
Classic Neighborhood Games
Get your kids away from the TV and video games and into the fresh air to play some classic outdoor games with children from the neighborhood. They'll have fun and get some exercise at the same time. Games that ages 7 through 13 can play together include hide and seek, Red Rover, freeze tag, kickball, and Ultimate, which uses Frisbees or other brands of flying discs.
Card Games
If you have a deck of playing cards lying around the house, then your kids have an afternoon of fun waiting. Cards are also a fine way to pass the time on long car trips. There are myriad kid-friendly card games, some of which help hone math skills. Games they can play with regular playing cards include Go Fish, Crazy Eights, Double Solitaire, War and Old Maid. Some games that use specialized cards and are apropos for kids 7 to 13 include Uno and Mille Bournes.