Would it be rich text when I copy to WordPad and HTML when I copy to a web page? Would it also support Markdown and maybe wiki ML? Would IntelliJ know that when I'm pasting code to an Emacs buffer in java-mode it should paste plain text, but when I'm pasting to an Emacs buffer that is an email, it should instead add org-mode annotations?

Overall this concept of copy/pasting with context is nice, but it only works for applications that have a defined API between them, such as MS Office OLE objects. In all other cases, pasting plain text is better than any "smart" solution.