We just released a fix for the After Effects CC (12.0) crash on Mac OS X v10.9 (Mavericks):
IMPORTANT: The After Effects CC (12.0.1) update fixes a crash on Mac OS X (v10.9). There is no need to install this update on any other operating system. After Effects CC (12.1) is coming soon for all operating systems and includes this same fix plus many more features and bug fixes. This update is only available as a manual download (not through the Creative Cloud automatic update mechanism) to prevent users on versions of Mac OS X other than v10.9 (Mavericks) from installing it unnecessarily.
Be sure that you are signed in and have activated the software—i.e., ensure that you are not running After Effects in free trial mode. The update will not work if you are running the application in trial mode.
Adobe After Effects CS6 (11.0.3) was released a little while ago with this fix, plus fixes for many other crashes and bugs. Details: http://adobe.ly/AE_CS6_1103