Pressure results from particles moving around and hitting surfaces. The ideal gas law links the pressure of a gas to its density and temperature, such that the pressure is increased if the temperature is increased or the density is increased (or both). As mentioned in the previous comment the particles move about randomly, although gravity acts on them it doesn't dominate (just as people can freely walk around) and so pressure acts in all directions.
Pressure is dependent on depth in general because of weight. For example in the ocean, if you are 1 metre down you have the weight of just 1 metres depth of water above you, if you are 500 metres down you have alot more mass above you and so there is a greater force acting, which means a greater pressure (since pressure is the force acting per unit area). If you go up into the atmosphere you will generally find the pressure decreases since there is less mass above you the higher you go. The weight of the atmosphere and oceans is because of gravity so in this way the pressure is a result of gravity but the motion of particles is not always downwards so the pressure is the same in every direction.
Last edited by SDA; 13-06-2012 at 23:04.