Welcome to Adobe Forum,
You can run the Acrobat Cleaner tool :http://labs.adobe.com/downloads/acrobatcleaner.html & try to launch
Then if it does not work, you can try this
1. Move the cache.db file from the location Macintosh HD>Library>Applciation support>Adobe >Adobe PCD>Cache or in windows : C:\Program Files (x86)\Common Files\Adobe\Adobe PCD\cache and move the cache.db file on to your desktop.
2. Close and reopen the applciation, you will get a prompt to enter the serial key, enter it and check if Acrobat is still crasing or not.
3:Rename the OOBE folder from the location Macintosh HD>Library>Applciation support>Adobe >OOBE or for windows : C:\Program Files (x86)\Common Files\Adobe\OOBE and rename it to OOBE.old download .
Install the Adobe applciation manager from the Adobe website and it should work.
(Apple made the user library folder hidden by default with the 10.7 release you can access the hidden or the root library by navigating Finder, choose Go > Go To Folder
In the Go To Folder dialog, type ~/Library and click Go.
To view hidden files in Windows go to C drive> organize>Folder&search option>View>show hidden folders>apply >ok
Please let us know if it worked.