Exporting Transparent PNGs in Adobe Illustrator CS6

System:
OS X Mavericks (10.9.2)
Adobe Illustrator CS6 (16.0.4)

Symptom:
When exporting an AI file to PNG using the Save for Web dialog, the resulting PNG file does not have a transparent background.

Solution:
The Save for Web feature seems to save whatever you see in the preview box, so if the preview doesn’t show any checkerboard patterns that indicate transparent regions, the resulting file will not have any transparent regions either. To fix this, select “Show Transparency Grid” under the View menu, and then try “Save for Web” again. The preview should now display the checkerboard pattern in your transparent regions, and the resulting PNG file will also reflect that.