Found in the Petrified forest biome.
Trap-door Spider hides in 1 deep holes with a 'dust layer' block covering. Ambushes players that come within a 2 block range. Grabs the player and inflicts damage and/or poison. Will not leave it's hole and will hide when a player is out of range. Immune to projectile attacks. Usual spider drops I guess (unless someone comes up with something good).

Maybe make it drop something used for making pitfall traps?

Yeah, some pitfall traps would be fun - could make some bamboo spikes and stuff and other trap related things :)