Carrots have a fairly long life after harvest if they're stored properly -- anywhere from a month to a year depending on the storage method. Three places in your home keep them from becoming as limp as a rubber chicken: the refrigerator, the freezer and a basement or root cellar.
Keep Them Cold
Store carrots in a container with a lid and keep them moist to maintain freshness up to a month. Wash the carrots and cut off leafy tops. Either fill the container with water and change it out every few days, or wrap the carrots in a moist paper towel, replacing it with a new one every few days. Put the container on the lowest shelf in the refrigerator. To freeze carrots, wash, peel and cut them up, then blanch them in boiling water for a few minutes. When they're cool, pack the carrots in freezer bags or jars. Frozen carrots can stay good up to a year.
If you have a root cellar or basement that stays cool, carrots can stay fresh for up to several months without taking up freezer space. Cut off the greens but don't wash the carrots. Put them in a container within layers of damp sand. Make sure they're covered completely with sand, and don't let the sand dry out.