Searched the net and found someone talking about possibly caused by this third party plug-in called "VectorScribe" - which I have absolutely no idea what the hell is that. Followed the discussion to this company called "Astute Graphics" to download a patch. But in the end, instead of fixing the problem, it caused more annoying issues which I will cover later.
Finally found this help page from Adobe about Illustrator crash at launch for OS X Mavericks (10.9). Followed the steps but it then complaints about Java 6 not installed even though I have Java 7 (1.7). After a few more search finally found the fix - just need to installed the Java for OS X 2014-001 and that fixed everything.
I then put back all those third party plug-ins which temporary moved out of Illustrator's plug-in directory. When I restart Illustrator, the annoying Astute Graphics stuff starts - huge popups occupying 50% of the screen as below, one after another - 12 of them in total.
Lesson learned, always check the official web site of the product for assistance first...