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: 
A positive particle accelerates along the electric field lines. If it came to an intersection, what way should it go?
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.