I hate this problem! There seems to be a simple solution that SOMETIMES works:
Possible Solution
Go to "Build Phases" → "Linking Binary Files to Libraries".
If you have a problem with say Foundation.framework. Just delete it i.e. Use the minus button ("-") at the bottom of the list.
And then add it again using the plus button.
Empty the build folder. (To do this, hold down the ALT key, then click “Product”> “Clear.” In “Clear Assembly” you will see “Clean” changes).
Another possible solution
Be sure to read Matthew's answer here ...
iOS SDK broken after reinstalling UIKit and Foundation databases not found
Look at the meaning of your "Search Paths Framework."
Another possible solution
Uninstall Xcode 4.3 completely and completely, use "CleanMyMac" (it will try to find every related component of the application that you are trying to uninstall).
Then just use the App Store to (re) install Xcode. As David mentions, this can sometimes fix this damned problem.
Why is this happening?...
I believe this problem can occur in situations where you, say, replaced your hard drive (i.e., probably using Cloner Carbon Copy Cloner or the like) or in some way the main volume on your Mac is renamed or changes in some way. I think that a small error may occur in the new Xcode "application-style", where it sometimes makes, and sometimes does not understand, such changes in the paths.
I hope this helps someone!
This is a causeless problem. I simply repeated this in this case, because subsequently I deleted a copy of the “old-style X-code” from the machine. (It might be best to remove the old-style XCodes (developer directory, etc.) before installing the new-style Xcode.)