IPhone – how do you backup iphone when some of the apps have the old style appleid

On your iPhone, go into Settings -> Store, sign out of your old Apple ID and sign in with your new one.

Your iTunes ID is the same as your Apple ID. I've recently switched email addresses as well, so I can confirm that you can easily change the email address.

Assuming that you've already successfully changed your Apple ID, follow the steps that Hand-E-Food mentions:

1. Go to Settings

2. Select Store (near the bottom of the section starting with General)

3. Click on your (old) Apple ID

4. Click on Sign Out

5. Click on Sign In

6. Click on Use Existing Apple ID

7. Sign in with your new Apple ID email address and password

   That's all there is to it!