Here's a list of a games that involve chasing, like Tag.  

Note that these categories are pretty fluid and there is a lot of overlap between different ones.  Where applicable I've cross-referenced similar games.

Amoeba Tag Broom Tag Capture the Flag Catch One... Catch All Colored Eggs DareBase Drapeau Espionage Chasing Game Farmer in the Dell Flashlight Tag Freedom Freeze Tag Hospital Tag Jungle Gym Tag Kick the Can Kick the Can Variation 1 Kings and Queens Man Tag Mexican Hideout Octopus Tag Partner Tag Pies Pilolo Pom Pon Prisoner's Base Red Devil Sneak Up Chasing Game Spy Steal The Bacon Stop There! Swat the Fly The Wolf and The Easter Eggs Tiggy off Ground Toilet Tag TV Game TV Tag Up and Down Warewolf (a tag game) What's the Time Mr. Wolf