I have tried re-installing InDesign several times without solving the problem. In desperation, I purchased a new SSD drive, installed a new version of Mavericks, installed a new version of Creative Cloud, and a new version of InDesign. It still crashes almost immediately on launch.
For dtp center -- I too am having numerous problems with indesign cc 2014 -- first I was loosing files because they wouldn't open (various error messages) wasting a huge amount of time and now indesign crashes on opening. As much as I like CC, it's ridiculous to have so many problems like this with software. All of the solutions are idiosyncratic when it's clear that users are experiencing the same or similar issues. I don't have a solution but I hope that a solution (that really works) will be found.