The Federal Deposit Insurance Corporation, which insures bank deposits in the US against bank failure, recently conducted a large national survey, which CNN Money reported on. The FDIC survey itself is here.
FDIC believes that about 7.7% of US households, or 17 million adults in total, don't have a bank account. 20% of US households earning less than $30,000 don't have a bank account; the poverty line is $14,500 and $18,300 for families of 2 and 3 respectively, and families making under $30k are definitely near-poor. Nearly 18% of all households, or 43 million adults, use alternative financial services like payday lenders; the FDIC refers to these households as underbanked.
An estimated 22% of Black households, 19% of Hispanic households and 16% of Native American households are unbanked, compared to around 3% of White and Asian households. Similar disparities occur for underbanked households - 31% of Black households, 29% of Native American households and 24% of Hispanic households are underbanked, compared to 7% of Asian and 15% of White households.