Batting helmets are required for baseball players, from T-ball all the way up to the Major Leagues. Playing baseball in the backyard doesn't exempt you from the rules of the game, or the rules of physics. If you are going to use real baseballs and real baseball bats in the backyard, then batters need to wear helmets.
A lot of research has been conducted to improve baseball safety. In recent years, there has been an increased focus on eye injuries and other facial injuries from wild pitches and foul tips. The guidelines published in the journal Pediatrics encourage kids to wear batting helmets with a metal cage to fully protect the face [source: Warner].
If you're playing with a catcher, the catcher needs to also wear a full catcher's mask with a throat guard, chest pads and shin pads. Boys playing catcher should also wear a hard plastic athletic cup [source: Warner]. If kids are old enough to hit hard line drives, then all boys should probably be equally protected. It might seem like a lot of fuss for backyard baseball, but accidents and injuries are not confined to the chalk lines of a well-groomed baseball diamond. If you don't want to deal with helmets and pads, then stick to Wiffle and Nerf balls in the backyard.