Yes, I've wasted hours resolving this incredibly annoying issue.
If you've ever changed your user ID and/or apps were purchased on your device under any other ID than your main apple ID, then you will likely encounter problems.
Ironically, this came up because I changed my apple ID....when I started having login problems with multiple devices (Macbook, ipad1, iphone4s). Created new apple ID, verified and consolidated under one email and everything went fine as far as my laptop and iphone.
Then I picked up my ipad for the first time in several weeks and hello, it wants my old apple ID for an app update. It shows me logged in as my NEW ID but if go to update an app it asks for my old one. None of the clever fixes suggested worked and even updating to the newest OS didn't fix it.
What did work for me:
1) Delete the apps. If you are conscientious about backing up it's an annoying but they will reinstall when you sync.
2). Remember your old password! Shockingly, I discovered my old password under my old username still actually worked for the old apps purchased under said name. NOTE: Old apple ID's DID NOT require the first letter of your PW to be capitalized. This might throw you off if you like me have an ancient apple ID.
Good luck.