This was a game I sure remember playing as a kid and no doubt if were socially possible to today I would gladly. The game involves one or more of you chasing other players with the aim of touching them generally with your hands.
Two or more players decide who is going to be 'it' using a counting out game such as Enny Meany, miny, moe and the one designated 'it' then chases the others attempting to get close enough to tag them - a touch of their hand - that makes that person 'it' and so it continues usually to the end of recess at schools.
In some forms it's deemed if you are on or touching a safe are then you can't be tagged cos it's off limits.
There was a form of it I well remember well from primary school 'cos we played it all the time called Kiss Chase.
The main difference is the tag is done by kissing rather than a touch of the hand and typically all of us of one gender are 'it' at the same time and chase the others of the opposite gender until everyone is caught at which point the team that was caught becomes it.
I really loved playing kiss chase between 8 and 11 years of age.