Is there a way to add a web part property to every web part (SharePoint 2010), including OOTB web parts. Essentially I want to add a header color option to the appearance section of the web part tool pane. At first glance I do not think this will be possible.
By "add a property" you mean configure it? - If that is the case it should be possible. If the answer is rather NOT, but actually "extending" the WebPart definition with a NEW property, then you could make sure your own web parts use the same base WebPart.
And not for the OOBT web parts, unless you build Control Adapters and as soon as they will load you could insert your piece of code.
Hope it helps, C:\Marius