How to hide notification center button in Mountain Lion?

I am using Mountain Lion.

The only advantage (for me) over the gesture is that Option + clicking the button enables/disables showing alerts and banners (toggles the switch in the notifications center).

Is there a way to hide the button in the status bar that opens notification center?

I had the same problem yesterday, and found this tool called Bartender. It is paid software.

On my Mac, running Mountain Lion, the icon is gone but the other notification functionality remains.

Sadly we can't remove the icon yet without disabling Notification Center entirely.

Should you want to proceed, this procedure requires a short disclaimer.

Warning:
This involves hacking your System folder; make appropriate backups and proceed with caution!

Go to /System/Library/CoreServices and select Notification Center.app. Press ⌘I to Get Info. Click the Lock icon at the bottom of the screen to unlock the settings (you will be prompted for your password). In the Sharing and Permissions portion of the pane, click the plus sign. Add your account as a special user, then set the Privilege column to Read & Write for yourself. Then, in the Name and Extension field, add the letter x to the beginning of the file name, dismissing any warnings the system throws your way.

Reboot the system.

If you don't want to reboot you can use Terminal.app, which can be found under /Applications/Utilities/Terminal.app. Type killall NotificationCenter and press enter. This terminates the NotificationCenter process.

Note that this eliminates the icon, but also all Notification Center functionality.