Q: I removed a Windows 8 Mail application mail account that was replicated from my other machines, but the account reappeared again--why?
A: Windows 8 features the ability to sync various types of settings between machines for a user account associated with a Microsoft ID (formerly known as Live ID). Among these settings are application settings such as the mail accounts.
It seems there is a "feature" right now that enables the following to happen: Even after you remove an account from Mail (and therefore calendar and contacts as well) just for the current machine, it will actually replicate back to the machine again and reappear.
The only way to stop the account coming back is to do one of the following:

The downside to doing this is that it means other application settings won't replicate between your machines.
You might also be interested in my FAQ "Q: How can I force an update of my Windows 8 or Windows RT environment?"
See more FAQs at John Savill's page.