Well when you get a mail, a notification in the lower right pops up and even says what the subject is, who it's from and a little bit of preview text. You also get a sound.
Not big enough?
The same way as what people have already mentioned, they just use bigger graphics.
I doubt you would find something as flashy as what you saw in Mission Impossible for download. The majority (if not all) people on the Internet don't want their entire screen space invaded by a "you've got mail" notification everytime they receive an email.