Delete old email addresses? What do you mean -- do you want to remove email accounts that you no longer use from Mail.app so that they don't try and check for new mail anymore? Or do you want to remove email addresses for people in your address book that are no longer active? I don't quite understand...
As for "spam," or unsolicited email advertisement, you cannot stop it. You can only "filter" it with junk mail filters, like Mail.app's own junk mail filter. To cut down on the amount of spam you receive, NEVER, EVER put your email address into any forms on the internet.