They are many and all of them beautiful. Deciding which type to grow is up to you, and your environment for growing be it indoors or out, hot and dry or wet and cool.
Here is a sampling of the various poppy varieties:
"Paeoniflorium" types-Burnt Orange, Crimson, Flemish Antique, Pink Chiffon, Frosted Salmon, Crimson and White, Kaladanthi
There are also several mixes of Peony Poppies-one is named Summer Fruits.
"Laciniatum" types-Aigrette, Crimson Feathers, Danebrog, Pink Bicton, Rose Feathers, Indian White-Rajasthan
"Single" types (which, by the way, are supposed to produce the best pods for drying)-Queens Poppy, Persian Princess, Imperial Princess
Other varieties include:
Tasmanian, Nigrum, Persian White, Hungarian Queen, Turkish Commercial, Hens and Chicks, India Black, Golden Triangle White, China White, India Bhandwa, Pepper Box, Crimson, White & Pink Clouds (doubles), Persian Gold, Austrian, Slavic Breadseed, Southern Belle, Natasha
This list will keep growing along with descriptions for as many as we can find. Thanks to May Wine for a sizable portion of this list.