With iOS 6, you are given more granular control over your various e-mail accounts. Just as you can for each of your e-mail accounts, you can adjust notifications on a per account basis.
To get started, go to Settings > Notifications > Mail and you'll see your e-mail accounts listed along with a line for iOS 6's new VIP feature.
Tap on an account and choose whether it should be included in the Notification Center. You can also choose your preferred alert style (none, banners, alerts) for the account. In the third section from the top, you can choose whether new messages should arrive with a badge icon or sound alert. Lastly, you can choose whether you'd like the banner or alert notifications to include a preview of the message and whether alerts should show up in the lock screen.
This degree of customization can be beneficial if you have an e-mail account that gets lots of useless e-mails every day. Or, if you received an iPhone from work, you could add a personal account but receive notifications for only your work account.
One thing I've done is turn off badge notifications for both of the e-mail accounts I set up on my iPhone and then turned on badge notifications for only VIPs. To do so, switch the slider off for Badge App Icon for each of your accounts, and then tap the VIP menu item listed below your mail accounts on the Settings > Notifications > Mail page and make sure that slider it set to on.
For more on Apple's new mobile operating system, check out our complete guide to iOS 6.