I recently opened an account with "ING Direct," doing everything on-line. I really use it for savings - I haven't set up an ATM card, etc., but I believe they offer a full menu of account options. Their website is at http://home.ingdirect.com/

I am not entirely sure how a U.S. bank would handle an account for someone who does not have a U.S. Social Security number - that number is required for tax purposes. Maybe others on this board would know - particularly any Canadians in border towns.