We would require more information to determine the cause.
Do you receive any error messages when the application quits?
What operating system are you using?
Do you have any earlier versions of the product installed?
Thanks, sorry for lack of info.
I'm using mac OSX 10.7.3 on a macbook pro 2.3 core i7
I have CS5 already installed and have also tried uninstalling illustrator cs6 and installing again, but get the same problem - the icon appears flashing in the dock but then quits and I get the standard 'Adobe illustrator CS6 unexpectedly quit' message
This document contains a list of troubleshooting steps to resolve launch issues:
I recommend following the steps provided for Mac and then trying to launch / reinstall the application.