I was able to get an E*TRADE cash/brokerage account with debit card without an ITIN or SSN, using my foreign address during the process.
A few useful things about it:
- No monthly maintenance fee
- E*TRADE Mastercard debit card
- the card can be mailed to a US mailing address (or maybe even foreign)
- supports bill pay can be used to pay credit cards
- comes with ACH and routing number
- unlimited ATM fee refunds worldwide (yet to be tested)
For non-US residents, this can be a pretty practical option if you just want a light, easy-to-get US banking for basic payments, debit card use, ATM access, and paying US credit cards.