A Creeper who has found a player will chase down that player until the distance between them is only a few blocks (It isn't going to stop until you get out of range or kill it so be prepared). It should be noted that Creepers tend to walk to the right of a player. The Creeper makes use of a suicide-bomb attack involving getting within close proximity of the player (usually 2-3 blocks) before exploding. The player's only warning to when they are about to explode is a very distinctive hiss and the swelling and flashing of the Creeper itself, which starts about 1–2 seconds prior to the explosion. It takes three full seconds to detonate. After it explodes, it leaves a large crater in the ground. The size of this crater is solely dependent on what the terrain is made from. Typically a hole in the topsoil is created, however, they can be powerful enough to destroy stone. When killed by an arrow shot by a skeleton, it will drop random Music Discs, which can be played in a Jukebox. (It doesn't matter who dealt most of the damage, as long as the last blow was the arrow of a Skeleton) This mob can not use doors but can climb ladders, unlike other hostile mobs.
Creepers can be somewhat formidable foes when encountered, as their stealth gives them the upper hand. Creepers are slow however, and will also reverse their detonation time if the player leaves their range; this can be used to the player's advantage in melee combat. The player can simply use their Sword and quickly back away before detonation, getting at least two hits in before having to retreat. If this process is repeated, a Creeper can easily be defeated.
The most effective way to eliminate a Creeper is to simply use a bow, as ranged combat will surmount the creeper's slow speed. Although with a regular bow the player would need at least three arrows, this can be minimized with enchantments. Another effective way is to light the ground on fire with a Flint and Steel and lead the Creeper up to it.
As of 1.7 the player can now hide from Creepers (And presumably other mobs) in double tall grass or double ferns. It is unknown why this happens (This may be a bug; it is unknown whether Mojang will fix it or not) but can be done. If the player is being followed by a Creeper, they can stand behind a double tall plant and crouch (It will not work if you don't crouch). The Creeper will be unable to see them and return to wandering around.
The crafting recipe for a creeper's arms, legs, torso, and head require gunpowder in the proper slots. (Pictures coming soon.)