Q: Our family has a shared computer with itune software. We have multiple apple devices and multiple itunes accounts. Can we share the computer and iTunes software to back up each apple device separately?

Hi Goodguy147,

Welcome to the Support Communities!

The easiest way to have multiple users with multiple devices share a single computer is to create a User Account on your Windows PC for each person.  Each person should also have a unique Apple ID.  That will keep each individual's iTunes Library separate from the others and each individual can associate and backup several devices to their iTunes library. 

Using your Apple ID for Apple services

http://support.apple.com/kb/HT4895

The article below is a troubleshooting article for Windows.  I'm just quoting the section from it that explains how to create user accounts:

iTunes for Windows Vista, Windows 7, or Windows 8: Fix unexpected quits or launch issues

http://support.apple.com/kb/ts1717?viewlocale=nl_nl

Follow the steps below to create a new user account in Windows Vista or Windows 7:

1. Choose Start > Control Panel.
2. Open "Add or remove user accounts." (If you're using the Classic view in Windows Vista, open "User Accounts," and then open "Manage another account.")
3. Select "Create a new account" and follow the instructions to set up the account.
4. Once you create the new account, choose     Start > Log Off.
5. Log in to the new user account.

iTunes Store: Associating a device or computer to your Apple ID

http://support.apple.com/kb/ht4627

I hope this information helps ....

- Judy