My DH is a Cub Scout leader and he says that these are the most popular games:
Strawberry shoe lace race: competitors put one end of a strawberry shoelace between their lips and then put their hands behind their back. Somebody else shouts go and all competitors race to get the shoelace into their mouth without using their hands.
After Eight Race: similar to the shoelace race but start with an After Eight on forehead and it's the first player to get it in the mouth.
Blindfold shoe shuffle - Each person puts on a blindfold and takes off their shoes. They then throw them into a pile in the middle of the floor. The referee then jumbles them all up and then shouts GO! The first person to find their shoes by touch and smell alone and put them on is the winner.
Doughnut on a string: another eating with no hands race, this time with doughnuts hanging on a piece of string!
Post it shake: This fun game has the easiest set-up. All you need are post-it notes and a timer! First, have the players split up into groups of two or three. One child will stand still while their teammates cover them with as many post-its as they can. Once the timer goes off, count how many post-its are still on each player. The team that has the most post-it notes still sticking wins! Start another game by having each team try and shake off all their post-its. The team that shakes off all their post-its without using hands first wins.
Smarties race: Give each child two small bowls and a straw. Fill one of the bowls with small sweets like Skittles or Smarties and leave the other one empty. On the count of three, children must suck the sweets onto the end of their straw, and transfer them to the other bowl. You can either put a time limit on the game, whereby the children get to keep all the sweets they have transferred when the timer stops, or you could have a race to see who empties their bowl the fastest. If you are planning the race version, make sure everybody has the same amount of sweets in their bowl to begin with!
Balloon bulls eye: To start with, give every child a balloon to blow up, and ask them to hold the neck shut rather than tie it in a knot. Place a biscuit in the middle of the floor, and on the count of three, everyone releases their balloon. Whoever's balloon lands closest to the biscuit gets to eat it! If you didn't want to play this with biscuits, you could also use trading cards or stickers as the target.
Balloon shaving: Give everyone a balloon and marker pen. They now have two minutes to draw a face on their balloon, and then apply shaving cream over it. Then give everyone a plastic knife for their razor. On ‘Go’, players now shave their balloon – only without popping it. The first person to do that is the winner.
Jelly relay: divide players into two teams. Give each team a tablespoon and an empty bowl. At the other end of the room/garden, place a bowl full of jelly. Teams race back and forward to see who can get the most jelly in their bowl within 5 (or 10) minutes.
Paper bag pick up: Your prop is one paper bag in the centre of the room, opened up full and standing up. Get the competitors to stand around the bag in a circle. The aim is to pick up the bag without using hands, arms, feet etc and without kneeling down (ie they have to pick up the bag in their mouth by leaning forwards). Each person gets one attempt otherwise they're out of the game. Each time you've gone round the circle, fold the paper bag over one fold (making it smaller) and then repeat the process. The winner is the one who lasts the longest! This game can be adapted for those who are differently abled (put on a table for example). This game was also done with a cereal box and 1cm / 1 inch cut off each time you go round the circle.