I skipped installing KB2862330 - Security Update for Windows 7 for x64-based Systems, and installed the rest of the updates and now my PC is running normally again as it was before. No more Blue Screens.
Microsoft references Update KB2862330 in Security bulletin MS13-081:
MS13-081: Description of the security update for USB drivers: (2862330) October 8, 2013
https://support.microsoft.com/kb/2862330/en-us
and:
MS13-081: Vulnerabilities in Windows kernel-mode drivers could allow remote code execution October 8, 2013
https://support.microsoft.com/kb/2870008/en-us
warning in both that after you install KB2862330, your computer may restart two times.
It looks like this update for USB drivers/kernel-mode drivers wreaks havoc on some PCs. It's no wonder I got a STOP 0X000000CA Blue Screen.
Microsoft should have tested this update more thoroughly. Now the question is when will they come up with a proper replacement that doesn't cause any problems.