I've Done Something That No One Else Has Done
Go around the room and have each person give a short introduction about themselves and have them state something that they think no one else in the room has done. If they state something that someone else has done, then they need to come up with something else that they think no one else has done.
Split everyone up into groups of 5 or more and then tell everyone to get in line in order of their birthdays (or alphabetically by first name, shoe size, hair length, age...) without talking. The first group to finish wins! Another variation on this is to have everyone line up in height order but have them all blindfolded. They are allowed to talk in this variation. This activity can be repeated multiple times with different criteria.
Form a circle, the first person to go will state and a word that describes themselves that starts with the first letter of their name followed by his/her first name (i.e. Giant George or Cooking Cheryl). The following people to go will need to state all the previous people's names and finish up with their own name. If someone messes up, the previous person that went has to repeat their turn and the game continues from there. The last person to go will need to state everyone's name and then finish up by stating his/her name.
Divide the group into two teams and have each team line up. An orange is placed under the chin of the first person in line of each team and they have to hold it between their chin and their chest. When the game starts, the orange has to get passed all the way down the line without anyone the use of anyone's hands and without dropping it. If someone drops the orange or uses their hand, they have to start from the beginning of the line again. The first team to reach the end of the line wins.