TYPE 1. THE PERPETUAL FOREIGNER
Asian/Asian Americans always seem to be foreigners to this country. Despite the fact that many Chinese, Japanese, and Fillipino immigrants have been here since 1840s. Many second or third generation Asian Americans are constantly bothered by “where are you really from?” and “you speak English really well for an Asian!” (true stories). And the media doesn’t help in perpetuating that idea either.
Exhibit A: How I Met Your Mother Season 5 Episode 3, Robin 101
Japanese speaking Shin-ya, played by a Japanese actor, Kazu Nagahama.
Robin barges in on Ted giving Barney classes about how to date Robin. Robin confronts them, then asks who “that guy is.”
Ted: He’s sort of been auditing the class.
Robin: What?
Ted: Well I tried to explain to him that it wasn’t a real class, but I don’t think he speaks much English.
TYPE 2. THE SHY QUIET GIRL
Often derived from the submissive, obedient Asian female stereotype. The Shy Quiet Girl never fights. She probably has pigtails or some other childlike quality about her. She usually cries or runs away from conflict.
Exhibit B. How I Met Your Mother Season Season 5 Episode 14, Perfect Week
Ted reads off names from the sign-up list, including the name “Cook Pu,” which he assumes to be a joke. Cook Pu says in her quiet whimpering voice, “Here.” Eventually a guy next to her tells Ted that she’s an actual person. She then proceeds to run out of class, crying.
Later in the bar, Ted hears an order for Cook Pu, which he assumes to be a prank by the other members of his gang, until Cook Pu says again in her quiet voice, “Here” and grabs her food.
She never once confronts Ted or even attempts to brush it off, she whimpers and eventually drops out of Ted’s Architecture class.
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There are of course other types such as the Ying-Yang Wise Old Guy, Ninja Guy, Nerdy Computer Guy (although this has been long criticized and been slowly declining in number), and Super Hot Exotic Girl. We’ve seen them all.
Asian American Feminist 
The Cook Pu joke was terrible. First, what a mean situation to be in if it had been real life. Second, let’s acknowledge that it wasn’t real life and the writers of How I Met Your Mother named a character Cook Pu exactly just for the reason of making fun of her. Who hurt you, writers?!