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: 
Electric field lines are a visualization of the electrical vector field. At each point, the direction (tangent) of the field line is in the direction of the electric field. 

At each point in space (in the absence of any charge), the electric field has a single direction, whereas crossing field lines would somehow indicate the electric field pointing in two directions at once in the same location.

Field lines *do* cross, or at least intersect, in the sense that they converge on charge. If there is a location with charge, the field lines will converge on that point. However we typically say the field lines *terminate* on the charge rather than crossing there.
A positive particle accelerates along the electric field lines. If it came to an intersection, what way should it go?