U.S. Pan Asian American Chamber of Commerce (USPAACC)
20 scholarships for high school seniors, with various requirements.
Asian and Pacific Islander American Scholarship Fund (APIASF)
Another organization that offers more than a dozen scholarships. Most require that you be of Asian or Pacific Islander ethnicity (according to the U.S census), with a minimum 2.7 GPA. U.S. citizens or legal residents, as well as citizens of the Republic of the Marshall Islands, the Federated States of Micronesia and the Republic of Palau are eligible to apply. Some scholarships have additional or slightly different requirements.
Asian American Journalists Association (AAJA)
Multiple scholarships, all for students pursuing a career in journalism.
National Asian Pacific American Bar Association Law Foundation (NLF)
Several scholarships, but only a single application to be considered for all of them. You must be currently enrolled in law school to apply. Scholarships are awarded on the basis of "academic achievement, leadership potential and commitment to the Asian Pacific American community."
Asian Pacific American Librarians Association
The APALA offers a scholarship for U.S. or Canadian citizens or permanent residents pursuing a Master's or Ph.D. in information or library sciences programs. You must be of Asian or Pacific Islander heritage.
For more resources, check out this article from CollegeScholarships.org