Aloe vera plants, sometimes known as "burn plants", are renowned for their healing effect. This is due, in no small part, to the plant's high moisture. This, in turn, points toward the way many aloe plants die: Overwatering.
Aloe can tolerate being root bound fairly well, but if your plant has dodged the overwatering bullet long enough to develop hard, crusty soil that pulls away from the edge of the pot, this would be a good time to repot it. Also, if your aloe plant has sprouted pups--baby aloe plants--these should be removed, their roots gently worked away from those of the parent plant, then repotted in their own, smaller containers.
Spread out newspapers or large garbage bags to help catch any spilled dirt. Prepare the new pot--which should have at least one drainage hole and be shallow, but no shallower than the old pot, and at least 1 inch wider than the old pot--by adding an inch of gravel in the bottom, then filling the pot to within 1 1/2 inches of the rim with a "cactus mix" potting soil.
Water the aloe plant lightly, if necessary, to help soften the soil. If the plant's soil is hard and has bonded to the edges of the pot you can use a butter knife to carefully break the soil free from the pot edge. If the pot is made of flexible plastic you may also be able to free the soil by squeezing the pot's sides in various places.
Support the stem of the aloe plant with one hand as you lift its pot and tip the plant--and pot--nearly upside down over the newspaper or garbage bags you spread out in Step 1. Continue supporting the plant as you carefully lift the pot away from it. Make sure to pull only on the pot, not the plant itself.
Set the old pot aside and use the fingers of your free hand to carefully work excess dirt away from the aloe's roots.
Scoop soil aside in the new pot to create a hollow in the center. Use both hands to tip the aloe plant upright and carefully seat its roots in this hollow. Scoop soil over the aloe's roots and add soil, as needed, to fill the pot within 1 inch of the rim--but don't pat the soil down to firm it.
Water the aloe plant lightly. Most aloe won't need more than a cup or two of water under any conditions, even less in the winter, so make sure not to overdo it.