MS Outlook (which I use at work) always displays the 'new mail' icon on the task bar when a message arrives, even if that message is immediately deleted by my filters. I am on several lists where I auto-delete about half the messages, and it is rather annoying for Outlook to tell me that I have new mail when really there is nothing new in my inbox. Apparently this is known to Microsoft and they just don't plan to do anything about it.