Volleyball
This game is the same as regular volleyball except that each team has a sheet or towel in which to catch the water balloon "ball" with and return it to the other team. All members of a team hold edges of the sheet and toss the balloon over the net, which can be something as simple as a rope tied across the yard. The other team the returns it the same way. The team with the fewest popped water balloons wins.
Tag
Fill up your water balloons, pick an "It" and run for it. The "It" has the water balloons and chases the other players. Everyone he hits is out. The last player left unhit is the winner.
To spice it up, give each player a water balloon to defend himself. They can use the balloon to hit the "It" player and distract him for the split-second it might take to get away. You also can make it so that when someone is tagged, she joins the "It" and chases the remaining players with her own water balloon. The rules are flexible. Be creative. There are as many options as your imagination will allow.
Trouser Stuff
Fill a tub with small, thin water balloons. Get two triple extra large pairs of sweatpants and divide the players into two teams. Have each team choose one member to wear the pants, then give the players a set time, such as one minute, and have them stuff the sweatpants with water balloons. The wearer must then race down to the finish line. The person with the fewest popped water balloons wins the game for their team.