What computer platform? What is the exact message you're getting when you try to package?
Have you tried restoring your preferences? Here's how:
Does this only happen in one file, or in other files as well? If only one file, try saving as IDML and reopening up the file. It could have become corrupted.
I had this problem once, it was caused by filenames containing "/" as many Mac user add as part to their filenames.
Another problem was once a network problem, where it stopped coppying files if they were bigger than a specified size.
It was never caused by InDesign.
I have OSX 10.9.2. I did a software updated for this on Wednesday as well as an InDesign CC update around the same time. Ever since then it will not package my links and it worked fine before this, so it may be the OS update causing the trouble. It happens with every file I try, and happens when I try to package a file to a shared network drive or on my hard drive. The message that comes up is 'cannot copy necessary linked file(s)'
Thanks for the tip - I will try to restore my preferences.
It could be a permissions issue. Open Applications > Utilities > Disk Utility. Run Repair Disk Permissions.