Adobe Flash cookies can be described as the cookie trail you probably never knew existed. And because the cookies are held offiste, by Adobe, even clearing your cache constantly won't stop your being tracked. As discussed in this April help guide, Browser History Sniffing and Other Tracking Techniques, putting the crunch on Adobe Flash cookies requires using Adobe's onsite management tool.
Recently, a team of researchers from multiple universities published a pilot study titled Flash Cookies and Privacy. In the study paper, the researchers noted:
We find that more than 50% of the sites in our sample are using flash cookies to store information about the user. Some are using it to 'respawn' or re-instantiate HTTP cookies deleted by the user. Flash cookies often share the same values as HTTP cookies, and are even used on government websites to assign unique values to users. Privacy policies rarely disclose the presence of Flash cookies, and user controls for effectuating privacy preferences are lacking.
The author's also note the widespread use of Adobe Flash Cookies among the top 100 Web properties, the fact that the use of this type of cookie is not consistent with user expectations, and further note that few tools are available to prevent this type of user tracking.
I have not read the other articles yet, but I am not sure whether or not Adobe is, or is not, responsible for this – or if it is Flash.
Flash is merely the technology used. Adobe owns Flash.