Could your eyesight improve natually so that you no longer need your glasses?

Not possible : In a word, no. Anyone who has a refractive error (nearsighted, farsighted, astigmatism), must use some form of correction (glasses, contact lenses) to have normal vision. There are various refractive surgical procedures available which can permanently correct one's vision so that glasses and contact lenses are no longer needed to have normal unaided vision.

Second Sight: Most of the time, the answer is no. A small subset of the population, that has low-power or latent hyperopia, will go through a period when the near vision improves spontaneously as a cataract develops and causes a myopic shift. This situation is not very common, but can essentially neutralize the effect of presbyopia. A routine eye examination is indicated. See index of refraction of the lens.