This report is interesting: it analyzes the trend in student (F1) visas issued by the US embassies and consulates in various countries. It covers the period 1998 to 2006.
The number of student visas issued to Indian and Chinese students in 2006 was double the number for 1998, with roughly more than 26,000 visas issued for each country.
In India, government and private sources have been providing students with more grants and loans to pursue international education. In China's case, an unusually large percentage of students in the U.S. study at the graduate level and are thus more likely to qualify for teaching and research positions that can reduce the cost of their tuition, thus removing a major barrier to seeking an education in the U.S.
This report points to this page on the Open Doors website with country-specific information. The Fact Sheet for India (doc) tells us that in the year 2004-05, there were nearly 80,500 Indian students studying in US universities, making India "the leading place of origin for students in the United States." A huge majority of Indian students (72 %) were in grad schools, with 20 % pursuing undergraduate courses.
Thanks to Scott Jaschik of Inside HigherEd for the pointer.