For clarification, gaming consoles and computers have used many different types of media over the years. These different formats have been converted into digital formats called ISOs, ROMs, Images, and few other things. For the purposes of this article I will just refer to them all as "ROMs".

Public domain and homebrew ROMs are available to the public for free; usually with a stipulation that they are never used for commercial purposes. Homebrew is a name given to games developed by (usually) amateur programmers who create these games for anyone and everyone to freely use and enjoy.

Although there are many freely distributable ROMs available for many systems; the vast majority of ROMs are "illegal".
Many call older ROMs abandonware; Abandonware is a name given to older games where the copyright holder no longer develops or actively tries to protect their copyright. These games may have been developed by companies that have since gone out of business. The truth of the matter is someone or some company still owns the copyrights to these games. The truth is no commercial ROMs can ever be “legally” downloaded. Unlike abandonware, modern games by Nintendo, Sony, Sega, Atari, Microsoft and others are actively protected. If you are caught downloading, or worse, distributing these games you will probably find yourself in court.

Every country has its' own laws concerning copyrights. In the US copyrights are generally good for 70 years (with filing extensions they can be good for nearly 100).
Example: The song “Happy Birthday to You” was copyrighted in 1933 and will still be valid until the year 2030. Many countries do not acknowledge or enforce copyright laws; these are generally where servers of websites that host ROMs are located.
Another clarification that needs to be made is copyright infringement is not a “criminal act” it is a “civil wrong”.
The difference being?
If you commit a crime you will be tried and go to jail. If you commit a “civil wrong” you will be sued and have to pay fines and damages to the copyright holder.

The truth is, even though ROMs are illegal, you are unlikely to have the FBI beating down your door for downloading Galaga, or Space Invaders. Actions such as this are generally reserved for those distributing illegal copies of the latest Nintendo DS, PlayStation 3, or Xbox 360 games.

In conclusion:
Are ROMs legal? Usually, No.

The simple answer is yes.

The legality of emulators was first established in 1982 when Coleco released an expansion module that allowed Colecovision owners to play Atari VCS (2600) games on their gaming system. Upon its release Atari immediately filed a lawsuit and sought an injunction against Coleco. In the end Coleco was found to have committed no copyright infringement and the module continued to be sold. In the late 90's Sony filed, not one, but three lawsuit against Bleem, a PlayStation emulator. The final ruling of Judge Charles Legge of the 9th U.S. District Court was that Bleem did not violate Sony's copyrights and the sales of Bleem continued.

Emulators can violate copyright laws when they are distributed with the original BIOS of a gaming system or computer (BIOS is an acronym for Basic Input Output System). Keep in mind that many emulators require a BIOS file to work but as long as the BIOS is not distributed with the emulator they are perfectly legal.

Quote:
This quote from Citizendium sums it up pretty well other than the fact that emulation is not always for obsolete systems. There are emulators for modern gaming consoles (PS2, NDS, PSP, etc).