* UPDATE: 04/11/2016 *
The updated method to re-arrange the Mac X mail accounts in 10.11 El Captain - please see below.
Open Mac Mail. Where your accounts shows up under "Inbox", simply highlight any account and drag it accordingly. See picture below.
No longer can you drag and drop your mail accounts in an order within Mac Mail. There is a trick to get the order of your mail accounts to stay in an order you define.
In Mac Mail, open Mail -> Accounts
Click on each Mail account, and then uncheck the Mail option in the panel to the right. Then, go through each mail account again, and re-check the Mail option, in the order in which you want...