These are the basic rules for three tag games, but make new rules or modify the rules as you like!
MINOTAUR TAG. Make a maze outside by mowing paths in long grass, laying down rope and garden hoses, or raking leaves into thin strips to represent walls. The person who is “it” gets a pool noodle, stick, broom, etc. that they can move around the maze to block a path to trap players. Players are after treasure items the minotaur hides in the maze. Whoever gets the most tokens in the time limit wins unless the Minotaur catches everyone before then (first person caught becomes the new minotaur). To speed up the game, once someone is caught they become a minotaur too (similar to “Sharks and Minnows” swimming pool tag). You might push sticks into the ground on corners–this helps avoid players arguing about whether someone cut corners.
ROCK, PAPER, SCISSORS TAG (rules here). For fun, invent three different things where each thing can defeat one thing, but lose to another. This creates funny confusion when teams try to remember what beats what and sometimes run away, but later realize their mistake. (“Stop running, our wizards beat their trolls!”)
FOX AND GEESE TAG. Make a maze with safe zone nests (use string, garden hoses, rake leaves into rows, etc., with sticks on corners to prevent cutting corners). Players race through maze to get food tokens they must return to their nest without being caught. If caught, they become the fox and the previous fox becomes a goose. Play until all food tokens are gone, or for a set amount of time, and whoever has the most tokens at that point wins.