By default when you get a new email message on the Mac, the mail icon in the dock is updated to include a red dot that tells you the number of new mail messages that you have waiting. You can also select an option in the preferences that allows a sound to be played when you get a new mail message.

But unlike many email and IM programs, there is no option in the preferences that allows you to bounce the icon in the dock when you get a new message. But if you want this, it is very easy to getting a bouncing mail icon on the dock. To do this, go to Mail -> Preferences and select the Rules tab. In the Rules tab, click the "Add Rule" button. Give the rule a name and in the pull-down for the condition, select the "Every Message" option. Then in the actions section, select the "Bounce Icon in Dock" option. Here's what your rule should look like:

The set-up for a mail rule that results in a bouncing mail icon when new mail messages are received.

Once the rule in configured, click "OK" and select "No" on the confirmation screen that asks if you want to apply this to current messages. Once you are done with that, you will now getting a bouncing Mail icon in the dock when you get new email. If you change your mind, just go back to the rules tab in the preferences and delete the newly added rule.