Why do waves spread in a definite direction? When we have a wave that is just transverse motion of molecules in water eg and if it is a circular wave, why does it spread outwards leaving the water behind motionless more or less? If you throw small e3nough stone into the pool you would make one wave that travels outwards in all directions, but outwards none the less....and this all started from a small segment of water which transfered its motion to all surrounding water. Why then doesnt the next segment pass its motion like that in all direction but only outwards? Is some kind of sum of small waves interfereing destructivly from each segment of water with the behind segment responsible for this? 
 A: A quick answer  is that systems act to achieve and maintain the lowest possible energy state. So by spreading outwards,  the energy of the stone is dispersed in the shortest time.
Systems act to offset and reduce the effect of a change in their former state.
A longer answer is:
From : Gravity Waves

Gravity waves on the surface of water are one of the most visible manifestations of fluid motions and one with which we all have a certain experience . The process at work is relatively easy to comprehend: A fluctuation causes water to rise above the equilibrium surface level, gravity pulls it back down because water is heavier than air, inertia acquired during the falling movement causes the water to penetrate below its level of equilibrium, and a bouncing motion results. The oscillation is similar to that of a spring that has been stretched and released.
The ‘spring’ action in a surface water wave is gravity, hence the name of surface gravity wave. What is somewhat less intuitive is why gravity waves propagate horizontally. To understand this, one needs to consider the horizontal forces at play. When a parcel of water rises somewhere above the surface, the added weight of this water creates a pressure that is locally higher than normal, and this pressure anomaly accelerates (pushes, so to speak) the fluid away from that place and piles it up a little further, generating another surface rise some distance away. The net effect is a translation of the disturbance, hence a traveling wave.

A: Well, think of it in terms of the atoms. When you drop a rock in water, the rock hits the surface more or less perpendicularly. It pushes the water in its way downward and sideways. It does this in every direction, so the wave also spreads out in every direction.
