If you're receiving your mail via a client program (such as Outlook, Outlook Express, Windows Live Mail or Thunderbird), rather than by using a web-based system, you can install Mailwasher to help prevent all types of spam from being downloaded to your computer:
http://www.mailwasher.net/
Further, by clicking on File > Properties > Details > Message Source (in Outlook Express - it's probably similar with other email clients) you can look through the headers to see where the mail really came from.
Also remember that:
(a) many (most?) banks don't know the email addresses of their customers (so they can't possibly send emails to them) ; and
(b) any legitimate email will start with something like "Dear Mr Coldicote" and not with "Dear Customer".
Chris