African-Americans:
Two and half million blacks registered for the draft. Just under a million actually served in the army. The highest percentage of black soldiers in the army ended up being 8.7%, even though 10% was the goal. The US military was very segregated in WWII. The units were divided into black and white units.
Doris Miller received the Navy Cross after Pearl Harbor. He manned an anti-aircraft weapon to defend against the Japanese, without having prior training. He was the first African American to receive the award.
The 761st Tank Battalion was African American tank unit. They could not legally fight next to white soldiers. Jackie Robinson was a 1st Lieutenant in 761st. He refused to move to the back of the bus, when commanded by a white bus driver. He never saw combat, but became one of the most famous baseball players of all time. The battalion led the advance in the Battle of Bulge.
Asian-Americans:
Japanese Americans were forcibly removed from their homes after Pearl Harbor because of US military's fear of sabotage. Many young, American born Japanese volunteered to serve for the US as the war progressed. The war gave Japanese Americans a chance to prove their loyalty to the US.
12 to 20 thousand Chinese Americans served in WWII. Three fourths served in non-segregated units.
Filipino soldiers found themselves on the front lines of battle from the beginning. They were commanded to protect every Philippine island.
Only about 100 Koreans enlisted in the Army. Fred Ohr became the only Korean fighter ace in WWII, and the only Korean-American in history to become an "ace."
Sources:
http://en.wikipedia.org/wiki/Military_history_of_African_Americans#World_War_II
http://en.wikipedia.org/wiki/Military_history_of_Asian_Americans#World_War_II
http://en.wikipedia.org/wiki/Japanese_American_service_in_World_War_II
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A bit brief overall and be sure to include personal thoughts.