Iris is a perennial plant with about 260 to 300 species, named after Irida, the Geek goddess, Iris has as many colors as there are in a rainbow, which explains why it is named after Irida - that name means rainbow. Iris Pallida and Iris Florentina (symbol of Florence, Italy) are often used in aromatherapy and medicine. The fleur-de-lys is based on the iris.
It is the root of the plant, the rhizome, that is used in perfumery, and that process of extraction is very time consuming, taking up to five years to get the essence. This explains why orris butter is very expensive. Because of the extraction from the roots, the iris note in fragrance is rooty smelling and very earthy on its own.
Two of the most famous iris perfumes from history are Guerlain Apres L'Ondee (iris and violets) and Jacques Fath Iris Gris (discontinued for many years and featured iris and peach).
The power houses of iris perfumes that are full-on rooty goodness are Serge Lutens Iris Silver Mist, Xerjoff Irisss, and Hermes Hiris. If you find those much too earthy and strange, a few iris perfumes that are rendered more classically beautiful through adding other notes are Acqua di Parma Iris Nobile, Parfums DelRae Mythique, and Frederic Malle Iris Poudre.
Good examples of iris perfumes that are soliflores are Chanel 28 La Pausa and Prada Infusion d'Iris.
Woody iris perfumes are The Different Company Bois d'Iris, Ormonde Jayne Orris Noir, and Van Cleef & Arpels Bois d'Iris.
Some other interesting iris perfumes are Cartier L'Heure Promise (iris and sandalwood), Parfum d'Empire Equistrius (chocolate, rice and iris) and By Kilian Flower of Immortality (iris and peach).
If you're on a budget, make sure to try out Hermes Hiris (linked above), Christian Dior Dior Homme (yeah, it says Homme, but it is definitely unisex) and Prada Infusion d'Iris (both a men's and women's version)
To get a more detailed article on iris perfumes, please check out Perfume Posse's Comprehensive Guide to Iris Perfumes.