Attack and defend games are quite popular in paintball.  There are many different variations of this game.  In one version, one team may be confined to an area they're to defend, the rest of the team may have a flag or treasure to capture for the opposing team and bring back to home base.  Either way, the basic point of the game is to defend your territory while breaking past the other team's defense.  One popular game is capture the flag.  In this play, the opposing team must lower the defenders flag and raise its own.  The opposing team has to raise their team's flag to the top of the flag pole.  If they are eliminated while raising their team's flag, the flag stays where it is and the station remains uncaptured until the flag is fully raised.  At this point, the defending team cannot recapture their station.  Another flag themed game is 'Attack The Fort'.  In this game, a fort is built up on a bunker.  Each team guards their own fort while trying to break past the opposing team's defense and get their flag to the tower of the opposing team's fort. 

Another fun variation (that doesn't include a flag) is the Bunny Game.  In this game, the team on defense has a fake bunny to protect.  The defending team cannot leave the defending area or conceal the bunny from plain view.  The attacking team starts off far enough from the defense that they are not in shooting range.  They are free to move around where ever they want as long as they remain in the boundaries.  The purpose of the game is the assassinate the bunny.  To win, the attacking team must shoot the bunny in the lens of its goggles.