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: 
Field lines are a visual representation of a mathematical construct, like a graph of a function. The defining properties of this visual representation are

1. The field lines run parallel to the field at every point.
2. The density of the field lines in an area is proportional to the strength of the field.

The second property tells you that the field lines can never cross. If they did the density at the point where they crossed would be infinite, and the implication would be that the field strength is infinite. This is unphysical.

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Here is one more way to think about it. What would it mean for two field lines to cross at a particular point? It would mean that the field had two different directions at that point. The [principle of superposition](http://en.wikipedia.org/wiki/Superposition_principle) tells us that the net field is simply the vector sum of the two. So the *total* field would only have one line going through the same point with a direction which was given by the sum of the two other directions.
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.