Question: The the title is self explanatory, I guess.

Why can two (or more) electric [field lines](http://en.wikipedia.org/wiki/Field_line) never cross?

Answer: 
The electric field at any point is the sum of all the fields due to each individual charge in the system. The field has a magnitude and a direction. The field lines are a representation of the magnitude and direction of the field over an illustrated area. The field lines point in the direction of the field. If lines from two sources were to cross, we could effectively sum the two fields at that point and redraw the field lines with the new direction. Thus, we can say field lines never cross because the sum of two vectors can only have one direction (with the exception of the zero vector)
Two electric fields line can never cross each other because at every point there is unique tangential direction of electric Fields.if they did, field at the point of intersection will not have unique direction, which is absurd.