Spiders are nasty mobs. They are quite fast, can climb walls, and they will still attack you in the daytime. They only spawn in the dark. When killed, spiders drop 1-2 fiber. Spiders mostly spawn in dark caves along with creepers and zombies. However if there is not much light and you are on the surface, they can still attack you.
Spiders will follow the player if they notice them. While they have no attacks, just being in the same block as them (or near them) will cause damage. Spiders are the only quadrupedal enemies and have the ability to climb up any vertical surface, even the player's home. And if threatened, they will follow you and can inflict nasty damage.
They climb cactus and take damage from it and thus can be used to make effective mob farms.