Running OS X El Capitan (10.11.2) on a iMac (27-inch, Mid 2010).
I updated InDesign 126.96.36.199 Friday, and today I cannot open existing files. I've restarted the computer, reset preferences, removed preferences, uninstalled and reinstalled InDesign, signed out of and back into Creative Cloud, and the problem persists. I'm working in a prepress department at a printing company, and I deal with customer files. I can't open the .indd files, nor their .idml files. Prior to this update, I had no issues with InDesign.
I've also tried using older versions of InDesign, and they are also affected: CC 2014, CC, CS6, and CS5. This part I cannot explain.
Update: I've downgraded to an earlier version of CC 2015, and I still cannot open documents. If I create a blank document, I can close it and then open it. If I attempt to open a document that I did not create in the last few minutes, I get a perpetually-spinning pinwheel cursor. Even files that I've used for months are inaccessible.'
Update: now the same problem is affecting Illustrator. I've tried doing this with Suitcase Fusion 6 running, and without, and it makes no difference.
Update: restarting the computer in safe mode seems to solve this problem, but using the system like this is painful. This is ridiculous.
It's something with your system.
Try creating a new user, and run InDesign and Illustrator from there. It's probably corruption in your user, or a third-party software conflict.