I did these yesterday and they both worked well with a group of mostly 2 and 3 year olds:
Put slips of paper in a drawstring bag. Tell child they are 'challenges' and they have to try to complete as many challenges as they are years old. Child draws out a slip of paper and tries to do what it says (things like "spin around", "stand on one leg", "pretend to eat an apple" etc). If they can't do it just let them choose another one. You can vary the challenges to suit the age of the children attending. At the end they get to choose a prize from another bag (I did packs of raisins which, being aged 3, they were pleased with, but I noticed cool small cars in Tesco's for under 50p this week).
The above worked well just going around the group asking who wanted to play, during general chatting and playing. However the real hit was the Tug of War:
15m of rope (from B and Q for 6 quid), tie a ribbon in the middle and put something on the ground as a marker for each team to aim to pull the ribbon over (a jumper will do). If you can get a few people playing to start with, everyone wants to join in. We played about 20 times and the children still wanted to carry on. If you have a mix of adults and children it works well, as the adults can control which side wins (best if agreed in advance to split wins fairly evenly) but the children still get to enjoy the sensation of strength and pulling as hard as they can. People did fall over a bit so I would only play this on grass or similar.
Hope these ideas help someone else.