How can I replcace the filename with file's creation date?

I have several photos with multiple filenames and I want to rename them by replacing the current names with the date each file was created. For instance a file named CAM00024 that was created 22-March-2013, to be renamed to 20130322 or 2013March22 or 2013-March-22.

If your camera saves the date in the metadata you can use ExifTool tags.
Tags vary between cameras but will be something like <ExifTool:DateTimeOriginal>
Select one of your images in the list and click the ExifTool button to see what is available.

The tag will probably return the time as well as the date but you can use an ordinary Replace method to remove unwanted text.

Alternatively you can use Date/Time tags that read the information from the file attributes. Note that Windows resets the Created date when you copy a file to the PC, so you should probably use "Date/Time Modified" tags.

It's all in the User Guide: www.advancedrenamer.com/user_guide/tags
and www.advancedrenamer.com/user_guide/exiftool