Why do electric lines of force never cross?

The short answer is if they did cross, they would represent a location with two different strong electric field vectors, something that can't exist in nature.

Lines of force represent the strength of at any given point. Visually the denser we draw the lines, the stronger the field is.

Electric field lines reveal information about the direction (and the strength) of an electric field within a region of space. If the lines cross each other at a given location, then there must be two distinctly different values of electric field with their own individual direction at that given location. This could never be the case. Therefore the lines representing the field cannot cross each other at any given location in space.

Examples If field lines were to cross what we need to do is merge them into a resultant field line. At each point in space we need to do vector addition on the field vectors from each source.

[Someone will have to confirm/correct whether it is correct to do vector addition with electric fields. If it is incorrect then we would perform vector addition on the force vectors instead and arrive at the same result.]