There are as many varieties of Asian hair as you can imagine--I am of Japanese and Caucasian ancestry so mine is super-thick, wavy, and grows black out of my head, but I've known a lot of Asians with medium to thin hair.  Texture can vary as well, but you never see Asians with naturally curly hair. 

Here are some commonalities to all of us Asians, which run the gamut from pale-skinned Japanese types like me to the perpetually sunny-looking Asians of warm places like Thailand:

1)Color: Asian hair is usually dark brown to black naturally.  I've seen hapas (people who are half-Asian and half something else like me) with light chocolate brown hair, but oftentimes Asian hair has red undertones.  Japanese women are especially fond of going blonde, and it is a fabulous high-maintenance look.  Once I had a Chinese friend who went bleach blonde.  The process took several days of repeat dyeing to get her hair from black to blonde and turned out to be a bit brassy.  Hard to maintain but cool.  A lot of Asians go prematurely gray as well.  I once dated a Chinese guy who went gray starting in his early 20s.  Tons of older Chinese women dye their hair black, probably to disguise gray. 

2)Thickness: This is the biggest variable.  I am blessed/cursed with thick, glossy, Asian hair.  It is so big that I cannot cut it any shorter than shoulder length without looking like I have a gigantic head.  Female-pattern baldness, however, is not uncommon in Asian women.  Lots of Asian women have fine hair that just gets thinner with age.  I don't envy these women, but big Asian hair like mine presents a daily battle.   

3)Texture: Mostly straight to slightly wavy, almost universally shiny.  Every Asian I have ever met has had glossy hair, whether he/she was from Myanmar or Japan.  Because mine is wavy, I envy Asian women with long, poker-straight black tresses.  Oh, so gorgeous.  My husband has a running joke that girls with the straight hair are looking at me saying, "I wish my hair had some waves like that woman!"  The grass is always greener.  Or blacker.  Curly hair doesn't really happen naturally on Asians because the shape of the hair shaft is curl-resistant and round.

Sincerely,
Queenie

My son is a half Asian(me)/Norwegian ancestory. His hair was light blond when he was born. The nurse nearly dropped him after she finished cleaning him up because she was so shocked by the hair color.

I've had people ask me if I do day care because my son's hair is so light. It's finially starting to get darker, a dark blond with reddish undertones. Now if only I could have hair as thick as his.