No, field lines never cross. This happens due to the very nature of field lines. We use them as an abstraction which shows us the direction of a vector field. If we think about an electric field, for example, we have situations such as the following
This indicates which direction a positive particle would go to, if placed on this field. If we had two lines crossing, it would mean that for a single point in space the particle would go to two different directions, which is not possible. This example is shown in the next drawing
From a different approach, if we think of field lines as a vector function for every point in space