Considered by many to be one of the best of all herbaceous perennials, A. frikartii, a cross between A. thompsonii and A. amellus, forms bushy mounds reaching two to three feet (60 cm - 1 m) tall and about half as wide. This one will tolerate part sun, so it can be grown in the sunnier areas of the shady garden. The fragrant flowers start blooming in summer and continue through fall. I've read that plants can be in flower almost year around in mild climates, but I take all such claims with a grain of salt. It's rated hardy from USDA zones 5 to 10, but will not be happy in the extreme humidity of Florida and Georgia. Divide every three or four years in spring.
The cultivar 'Monch' begins to bloom a bit later and is considered a superior selection.
Aster Tataricus
This one is huge, reaching six to eight feet (2 - 2.5 m) in height, with lower leaves to two feet (60 cm) long. Hailing from Siberia, it is hardy to USDA zone 3 and flowers in late fall. The cultivar 'Jin Dai' is on my 'lust' list! I'm a bit nervous about how well it would do in my USDA zone 7 garden, but if I can ever find it, I will just have to give it a try.
Another of the shorter asters, suitable for edging or the rock garden, the 'East Indies Aster' wants full sun, well-drained and fertile soil. It is somewhat similar to A. alpinus, forming tufts or mats a foot to eighteen inches (30 - 45 cm) tall and about a foot (30 cm) in diameter. It blooms in summer and is rated hardy from USDA zones 3 to 9. Flowers typically are blue to violet with yellow or orange center disks. The cultivar 'Wartburg Star' is one of several available.
Michaelmas Daisies
When people talk about asters or Michaelmas Daisies, they are generally thinking of either Aster novae-angliae, the New England Aster or Aster novae-belgii, the New York Aster. There are many cultivars readily available in the nursery trade although those of A. novae belgii are more numerous than A. novae angliae.