GNU Emacs is licensed under the GNU General Public License (GPL). The GPL is a copyleft license that requires any derivative work to also be GPL-licensed. Does that impose restrictions on what license can be chosen for third-party Emacs packages such as those found in MELPA and several other repositories around the internet?
I believe the answer to this question depends on the interpretation of the legal term derivative work: if a third-party package is a derivative work of GNU Emacs then the package must be GPL, else it can use another license. (Similar concerns have historically arisen with dynamically linked libraries.) I didn't find any clearly stated opinion on this matter on EmacsWiki, the Emacs Lisp reference manual or the GNU website.
In practice, we have third-party packages bearing e.g. the MIT license notice, but I wonder whether that license notice has legal clout and the real license ought to be GPL anyway.
derivative
does not appear in the text of the GPLv3. It actually refers to modifying the original program, where previous versions referred to creating a derivative. I'm not sure what the legal consequences of that are. In plain english, I think it's easier to make the case that a package is a 'derivative' than that it is actually a 'modification'.