I had never thought to even have a look at this until today. One of my good friends received his first Macintosh today (congratulations) and one of his first questions to me was, “Can I get the Mail.app icon to bounce when I have new mail?” I responded with an “I’m sure.” and opened the Mail preferences. After looking around for a moment it became clear that this wasn’t just a box to check.

I poked around and found a solution. If you go into Preferences > Rules, there is a panel much like a smart folder. If you change your settings to look like those pictured below, every time you receive mail, your icon will bounce in the dock.

This will pester and continue to bounce until attention is given so if you need to be working and not dealing with mail, you may want to turn this Rule off but if you, like me, are not a fan of system sounds, this is a nice way to be alerted of new mail.

Thanks to Aaron for the question!