Creepers are the bane of any Minecrafter, and a monster you want to stay sharply aware of, both in terms of what it can and will do, and in terms of where any are near you.
With their distinctive armless shape and mottled pale-green color, Creepers are hard to spot on grass, but otherwise very easy to notice. This is a good thing because they are a terrible hazard to anything nearby. On spotting a player, Creepers will head towards them in the same manner and with the same intelligence as a Zombie. This inherent directness and relative stupidity is a blessing, because otherwise they would be far more frequently fatal.
When a Creeper is less than two blocks away from you, it will emit a distinctive sibilant hiss- that sounds like something burning. There is good reason for this, as within a few moments after that, the Creeper will explode violently. This explosion not only destroys blocks (and likely you if you didn’t run for it the moment it sounded) but can also destroy the dropped items that blocks become as well, leaving a crater and not enough material to refill it. The explosion is powerful enough to break through a layer or two of stone, and anything less durable than that simply doesn’t stand up to it. This is not only painful in the damaging sense, but it tends to leave horrible holes in fences and buildings that then will need to be patched.
Just to make things worse, if a Creeper can see you through a window and you are within two blocks of it, it will still explode. That means that single-block-thick walls will not stop a Creeper from detonating- only from getting closer to you. It is for this reason that aboveground structures are often surrounded with fences despite sturdy walls.
While Creepers will be knocked away when hit just as any other monster or animal, that will not stop them from exploding, nor will it put them far enough away to keep you from being hurt when they do blow up. Only by standing far enough above a Creeper and reaching downhill to smack it when it jumps at you, or by charging it with a melee weapon to send it flying can you be truly safe from having a Creeper explode on you while you’re using a melee weapon. You will need to be careful, though- Creepers are twice as durable as you are, making any fight with a Creeper considerably longer than you want it to be.
If you manage to kill a Creeper without it blowing up, it will drop some gunpowder- which can be used to make TNT blocks. If you can trick a Skeleton into shooting a Creeper to death, though, the Creeper will drop a Music Disc.
Curiously, Creepers can be ‘supercharged’ by lightning in the same manner that Pigs can become Zombie Pigmen. Charged Creepers glow faintly blue, and explode with a much larger burst radius and amount of damage than a regular Creeper does, so be very very wary of them.
As one final note, Creepers will flee from wild Ocelots and from tame Cats- but not far enough to leave sight, so it is possible for a player with a pet Cat to accumulate a following of frightened Creepers..... a dangerous prospect at best.