CapitalOne 360 allows you to instantly open savings accounts and you can have many of them (not sure what the maximum is--it's high, I've had about 8 at once).

CapitalOne 360 allows you to instantly open savings accounts and you can have many of them (not sure what the maximum is--it's high, I've had about 8 at once). That said I liked the bank a lot better when it was ING Direct before they got acquired.