A Bow is one of two weapons (the other being the sword) that can be crafted in Minecraft. It functions as the primary ranged weapon for the Player (and the only one, aside from TNT cannons, that damages entities not counting Blazes and the Ender Dragon), giving them an alternative method of attack than the sword.
A Bow is an item that can be used to attack mobs, assuming the player has arrows in their inventory. To fire the bow, hold down right-click to charge the shot, then release to fire. The damage and range depend on how far back the arrow was drawn; for best results shoot at maximum charge. A fully charged bow will be known by two ways. First, the bow is fully charged when it stops the drawing animation and begins shaking, or the bow's arrow when shot will leave a particle trail, much like that of a critical hit when jumping with a sword.
The bow is best used to take on mobs at a distance or where sword attacks could endanger the player (such as engaging Creepers).
When fighting a Creeper or another mob, try to hit the block beneath it so you can keep a distance as aiming at the torso will slow you down and allow said mob to advance. Shooting from above ledges is the most effective way to kill mobs and/or a player, however when aiming stay close to the edge and sneak so you don't fall off the ledge. Bows are best used when fighting range attack mobs like Skeletons. The farther the bow is pulled, the farther the arrow will go.
Bow in PvP
Bows are an excellent initiator or full-length combat weapon if the opposing player is without one. The bow starts to lose its significance quickly when opponents adorn armor. To say that the bow is "over-powered" is clearly a matter of opinion. A shooter atop a tower would certain seem "over-powered" because the enemies can not reach him, however, on solid ground, sword wielders would easily run him down. To really keep the bow significant, enchanting the bow is nearly required of it in PvP, unless if is simply a defensive weapon in the defense of towers, walls, etc.
Flame (I) adds fire to the bow, said more simply making an arrow light on fire when it is ejected from an arrow and makes the cooked version of meat from cows, pigs, and chicken if they are killed by the fire.
Infinity (I) makes you have unlimited arrows so long as you have at least one arrow in your inventory.
Power (I-V) increases damage per shot. Only up to Power IV can be obtained from enchanting depending on the level, 30 being the max. In Survivla Mode, Power V can only be obtained by combining two Power IV enchantments from another bow or a book.
Unbreaking (I-III) increases the bow's durability. However, this enchantment is not the most useful for a bow.