I was having the same problem the other day - the App Store kept prompting me to enter a password for my boyfriend's apple ID every time I attempted to download updates. I use his computer/iTunes to back-up and charge my iPad and I guess it stored his account info the last time I had it plugged in (??)
To fix:
-go into Settings,
-click on your Apple ID,
-select "Sign Out" from the pop-up menu (even if it shows that your correct apple ID is currently signed in, which was the case for me)
-go back to the App Store
-try downloading a new app (you can delete later) or click the Update button for existing apps
-a blank username/password form will pop-up, allowing you to enter the correct apple ID info
I hope this helps - Worked for me and haven't had any other issues since!