The cortical microtubule (MT) array and its organization is important in defining the growth axes of plant cells. In roots, the MT array exhibits a net-like configuration in the division zone, and a densely-packed transverse alignment in the elongation zone. This transition is essential for anisotropic cell expansion and consequently has been the subject of intense study. Cotyledons exhibit a net-like array in pavement cells and a predominantly aligned array in the petioles, and provide an excellent system for determining the basis of plant MT organization. We show that in both kinds of MT array, growing MTs frequently encounter existing MTs. Although some steep-angled encounters result in catastrophes, the most frequent outcome of these encounters is successful negotiation of the existing MT by the growing MT to form an MT crossover. Surprisingly, the outcome of such encounters is similar in both aligned and net-like arrays. In contrast, aligned arrays exhibit a much higher frequency of MT severing events compared with net-like arrays. Severing events occur almost exclusively at sites where MTs cross over one another. This process of severing at sites of MT crossover results in the removal of unaligned MTs, and is likely to form the basis for the difference between a net-like and an aligned MT array.