This question has generated a lot of interest regarding whether or not we can talk about copyright in a general, international way. I argue that we can because copyright and IP law in general is based on international law. There are very few places in the world where the implicit copyright to creations is not granted, as has been the case since at least 1967. Even those countries that are not signatories to the Berne convention have other international agreements that follow similar patterns.
That is, this question does not ask "what is the extent of this law, and what are the penalties for breaking the law" (which would then require inquiring into local statutes) but rather asks a much simpler question: "is it, generally speaking, illegal to provide copies of this material, or come into possession of the material without express permission of the rightsholders?"
It is an uncomfortable, unalterable fact that, globally speaking and at this moment, it is against international law to share or possess such material. How that law might be interpreted, and the specific legal risks and implications of that law where you live is certainly open to discussion, but is not actually part of this question or this answer. Answers that provide specific examples of how countries interpret international law are helpful background but we do not need to consult local law to answer the specific question at hand.
TL;DR: sharing or downloading ROM images is almost certainly illegal, or at
least legally complicated. However, most rightsholders are likely not
interested in pursuing action against individuals.
I am not a lawyer. This is not legal advice. Intellectual property law at a local and global level is a complex subject most lawyers don't even fully understand. Trying to distill all of that into a single SE answer is a fool's errand.
That being said, some general comments about the legalities of retro system ROM images can be made by this particular fool.
Legalities will differ depending on your locale but, in general, downloading ROM images for any system (regardless of age) is strictly not allowed by law. In fact, it may even be considered "software piracy" to make images of ROMs you legally own. This is why emulation sites shy away from showing you where or how to get ROMs for their software.
There are locales, however, where it is legal to create and download copyrighted material for personal, non-commercial use. Check with an expert about your local statutes on the subject.
The inverse is also true: there is no global, over-arching law that governs or specifically allows downloading ROM images, especially those that make special claims regarding some specific number of hours that intellectual property can be in your possession.
And even if downloading an image is legal where you are (or is not specifically illegal, as the case may be), it's not like a particularly litigious rightsholder won't try to pursue legal recourse if they think they have a case. (Perhaps an unlikely situation, but words are small comfort if your ISP is suddenly pressured to disconnect you.)
Of course, there are many sites that offer ROM images of games and system firmware for download. These sites are almost certainly breaking the law (or are in a legal grey area), though in many cases the rightsholders may not have any interest in pursuing legal interests. Such sites may also be operating out of countries where it is legal to offer such services, or the legal recourse for rightsholders are limited.
Finally, I would be remiss if I did not link to the Wikipedia article on the legal implications of abandonware.
Whether or not creating or downloading old or abandoned images is adhering to the spirit of the law is up to individuals.