With the amount of storage space that Google gives for its mail service, you might wonder why you would want to backup your account. There are several reasons why this is not as strange an idea as it may seem.
First, it is bad IT practice to store too much information in any one place without sufficient backup. Accidents happen.
Second, if you find yourself unable to connect for any reason, a local copy can be quite helpful. Accidents happen.
Third, while the possibility may seem remote, Google reserves the right at any time to suspend your account without warning (see Section 4.3 of the TOS). "That won't happen to me - I haven't done anything wrong!" you say. Well, eh-hem, accidents happen.
Fourth, you may ultimately decide to move your mail to another provider and want to move all of your old messages as well. This tip will help you create your own Google Mail archive.
In order to download all of your mail from Google, you must first have POP access enabled. See Heinz Tschabitscher's guide on accessing your Google account via POP3 to affect this.