UPDATE: At the time of this writing, I was notified that this link is not completely correct. You may run into issues trying to do this.
A few folks recently pinged me. They're long time MS services users. They have gamertags that are several years old. When they set these accounts up, they didn't have another Microsoft account, or didn't want to use the same one. With the rise of the "Microsoft Account", we're adding a lot of features that depend on a common email address. Things like Windows 8, Windows Phone, Office 365, Outlook.com email, OneDrive, MSDN and more are all tied to your account. Your Xbox experience likely has game info, video content, music content and more. If your Gamertag and Xbox Live account don't share the same email address, your 3 devices, 1 screen experience isn't going to be great. You'll only be able to use some content from one location, or from one logged in user id. Fortunately, we do have a way to change your XBox Live email address, so you can associate it with your "new" Microsoft Account. You can do it at the link below. It will take some time, due to features that aim to prevent fraud and abuse.