One Person as "It"
Most games of tag center around a single person who is "it" and tries to tag the other players. Players who are tagged are usually out until the next round, and the last person to be tagged gets to be "it" on the next round. Examples include Freeze Tag, in which tagged players are frozen till another player unfreezes them, and Blindman's Bluff, in which "it" is blindfolded and tries to tag other players by listening.
Some tag games start out with one person as "it," but when other players are tagged, they become "it" as well. One example is Blob Tag, in which players who are tagged must join hands with the original "it" and run with them to try to tag other players. Another example is Catch One, Catch All, in which a player who is tagged becomes "it," and all the "its" can tag other players till none are left.
Multiple "Its"
Tag games with more than one "it" are games in which a team of players are all "it." Sometimes this is only a few players, such as "Sharks and Minnows," in which most of the players are minnows who try to run across a boundary guarded by two or three sharks.
Many of these have two teams of players who alternate being "it." One example is Giants, Wizards and Elves, in which two teams face each other across a center line. Before each round, each team decides whether they want to be giants, wizards or elves. They then face the other team, and on a signal, both teams perform a motion that represents one of the three peoples. Giants beat elves, elves beat wizards and wizards beat giants, and the team that beats the other then chases the losing team toward a boundary line, trying to tag as many members of the opposite team as they can. Tagged players join the team that tagged them.
Another simple version of tag with multiple "its" is Everybody's It Tag, in which every player tries to tag all the other players. Players who are tagged sit down, and the last player standing is the winner.
Changing "Its"
There are also versions of tag that have only one "it" at a time, but the person who is "it" changes continually throughout one round of the game. One example is Elbow Tag. In this version of tag, everyone hooks arms with a partner, except for two people who are "it" and the runner. "It" chases the runner. When the runner gets tired, he hooks arms with one of the people who is standing still. That person's partner then becomes the new runner. When "it" tags one of the runners, then that runner becomes "it," and "it" is free to hook arms with someone and send their partner as the new runner.