Japanese, Chinese and Koreans have a reputation for doing well academically, and are generally not treated as minorities if they were born in the United States. In fact, there have been reports of "reverse discrimination" in which Asian applicants were required to have higher LSAT scores and grades than their Caucasian counterparts.
Recent LSAC data shows that this "reverse discrimination" continues as a national trend, as I discussed in Race: Why it Matters and How Much.
This tendency to exclude Asians seems to be part of the myth that they are "taking over" our institutions of higher education. In fact, in 2001, there were about 78,000 applicants to law school. Of this number, 5500, or 7%, were Asian. In 2007, 6,000 out of 85,000 applicants were Asian, or about 8%. That these numbers are viewed as an "invasion" is more evidence of our prejudices than of an influx of Asian super-achievers. In 2007, Asians are declining slightly as a proportion of the applicant pool.
Vietnamese, Thai, Laotian, and Filipino people are generally recent immigrants, facing both economic and language barriers, and are usually considered to be disadvantaged minorities. However, in collecting ethnic data, many law schools only include "Asian" as a category. The new D.o.E. regulations about reporting ethnicity may change this, but as of 2010 it's too soon to know. You should skip right over to the section on "the New Asians."
The admissions officer from one east coast law school mentioned that Japanese students applied in lower numbers than Chinese or Koreans, giving them a slight advantage for diversity. I have no idea whether this is a national trend, however.