Which musical works can receive an ISWC?

Does the work have to be protected by copyright before receiving an ISWC?
No. ISWCs are allocated regardless of copyright status. Registration Agencies may adopt authors from the "public domain", according to their local laws, and assign ISWC numbers to their works.

This is generally done for reasons of national interest. For example, the traditional folk repertoire, works in the public domain whose authors are unknown, can be numbered by an authorised local Registration Agency.
Which types of musical works can receive an ISWC?
An ISWC may be assigned to any musical work, published or unpublished, newly created or already existing including but not limited to: dramatic musical work, musical arrangement of a work, adaption of lyrics of a work, translation of lyrics of a work, a recognised excerpt of a work, or a medley.

For the sake of clarity, a musical work is composed of a combination of sounds, with or without accompanying text. Text only (lyrics) works cannot receive an ISWC.
Should adaptations and translations get an ISWC?
Musical arrangements, adaptations of lyrics and translations must receive their own unique ISWC numbers. These ISWC numbers are usually allocated by the agency which administrates the works of the arranger and/or adapter. The connection between the "version" and the original work is indicated in the descriptive metadata of the ISWC.
May excerpts from other works be numbered too?
All works should be identified in their own rights. Similar to the "versions", the relationship between excerpts should be indicated in the descriptive metadata of the ISWC.

For example, an aria from an opera or a cadenza from a concerto can receive an ISWC.
May works or “versions” which breach copyright obtain an ISWC?
Surprisingly, the answer is "yes". The non-authorised arrangements of a musical work can be identified, if only to ensure that they will be recognised at an international level as works infringing the copyrights of others.