After Effects region of interest guest Paul Uusitalo (After Effects quality engineer) says that After Effects and the Adobe Crash Reporter need your help.
If you've crashed you may have seen this dialog, which is more convenient than later sending a note to aebugs @adobe.com. Instead of canceling, the AE team is asking for at least a short description of what you were doing at the time of the crash and an e-mail contact.
One CS4 bug that might come up on the Mac is a crash if you have the Script UI panel open when exiting AE. To fix this, undock or close the script-generated UI panel. Chris Meyer adds (update): "I found once I had crashed with them open, I always crashed even if I closed them in subsequent boots. I had to remove them, quit once successfully, reinstall them, then make sure I never quit again with them open."
You can also look at Mylenium's After Effects Error Code Database: Overview, Troubleshooting and Solutions, search the Adobe Knowledgebase (try "crash" in AE), and post on the Adobe Forums. Also, you're entitled to a certain number of free calls for "installation issues, basic usage questions, and troubleshooting unexpected behavior for documented features." There's also a chance the problem is on the user side, like bad RAM or something!
Update (Jan '09): Michael Coleman allays fears in Adobe Crash Reporter Privacy.