All chrysanthemums are perennials. The important question is whether they are hardy in your area of the country. The good news in that there are now a large number of chrysanthemum species and varieties that are relatively cold hardy and can be grown in USDA Zones 5 - 9 and some even in Zone 3. Here are some suggestions:

C. x rubellum 'Sheffield.' Hardy to Zone 5. Grows to 2 feet. Light pink flowers.

C. 'Prarie Lavender'.  Hardy to Zone 3. Grows to 2 feet.

C. 'Will's Wonderful'. Hardy to Zone 5. Grows to 2-3 feet. Strawberry red flowers. 

C.  x rubellum 'Clara Curtis'. Hardy to Zone 3.

C.  x rubellum 'Mary Stocker'. Hardy to Zone 4.

C. morifolium  Mammoth 'Daisy Bronze'. Hardy to Zone 3. Grows to 2 feet.

C.  x rubellum  Mammoth 'White Daisy'. Hardy to Zone 3. Grows to 18 high.

C.  'Bronze Elegans'. Hardy to Zone 5. One foot high. Apricot flowers.

C. weyrichii. Hardy to Zone 4. A dwarf species, growing to 8-12 inches. Pink flowers

The best time to plant these mums is in the spring. If you want to plant them in the fall (which has the advantage that you can select their true color) then cut off all the flower buds before you plant them so that they will put their energy into growing new roots and develop a good root system before winter. It is a good idea to leave the stems on the plants over the winter which helps to protect from winter damage. Alternatively the plants can be heavily mulched; this is good idea in colder regions.

Note that the flowering mums you find in your garden center or grocery store in the fall are probably not hardy perennial mums. Hardy mums are more likely to be found in nurseries in the spring. Some of the listed varieties may be hard to find in nurseries but can be purshased on line. Note also that the nomenclature of chrysanthemums can be confusing - they are sometimes listed under the genus Dendranthema. C. x rubellum cultivars are also known as Korean Mums.Also, the Mammoth series of mums are sometime found under the name My Favorites.

Courtesy of NYBG Plant Information