Generally, perennials should be divided during the season opposite that in which they flower. So spring and early summer bloomers should be split in fall, and late summer to fall bloomers in early spring. The idea behind this is that the new plants will be able to put all of their energy into root and leaf production, rather than flowering, and therefore have an easier time becoming established.
When dividing in spring, do it early enough that the plants will have at least several weeks to recover before hot weather arrives. When dividing in the fall, leave the new divisions four to six weeks to settle in before the ground freezes.
Many gardeners in the coldest climates (USDA Zones 3, 4, 5) do all of their dividing in early spring, so that the plants can use the whole growing season to develop a good root system before the onslaught of winter.
Whatever time of year you divide them, be sure to water your plants well the day before you divide them. Prepare their new locations before you dig them up, and try to divide and transplant them on an overcast day or at the end of the day, so they won't be stressed by hot sun.