As an old-school emu-geek, allow me to explain the full legality of emulation! This will be long.
Possessing ROMs
Emulated arcade and console games are stored as images of the cartridge or disc on which they were stored. These are called ROMs or ISOs (for discs). Arcade games can be made up of multiple roms stored in separate chip clusters but this is uncommon in older home consoles.
It is legal to own Roms in the following ways, without question:
-You have legally purchased the physical media containing the rom, be it a cartridge or a whole arcade cabinet
-You have been legally sold the rom by its license-holder
Fair Use tells us that it is legal to own roms of any kind if there is no other reasonable way to preserve the media within. For instance, if tomorrow every copy of Nightmare in the Dark is smashed and it is pulled from any online channels through which it can be bought, then you can legally download it since otherwise it would be gone forever. In this respect, the modern fad for virtual consoles (themselves just emulators) makes emulation thorny. For instance, you could for some time have made the argument that since no new Sega Genesis are being made, or copies of Sonic 2 printed, that having a sonic 2 rom was okay. Now that it exists on wii and Steam in the ultimate collections, it's not. A simpler way of looking at this is that if you have no way in hell of buying a game, and neither does any other normal person, having a rom is probably fine.
Playing ROMs
There are two sticky wickets in actually playing roms: BIOS files, and the Digital Millennium Copyright Act (the DMCA).
A BIOS is a file that in the original platform on which the game ran, managed the platform hardware. A BIOS in emulation is an easy way to cheat hardware compatibility, because that bios tells the emulated system how to behave. Without a BIOS, you must reverse engineer how the hardware behaved. The following classic consoles require bios files to emulate:
-Neo Geo
-Sega CD and 32x (although there is also a fan-made Sega CD bios)
-Some other arcade boards
-the PSX arcade platform, but oddly NOT the Playstation
Almost all consoles newer than the Playstation will require a BIOS for emulation. The only legal way to own a bios is either through fair use, as above, or the ownership of a physical console (or bios rom card from said console). Most BIOSs include provisions for distribution that require them to be running on original hardware. Fair use can be considered to trump this, HOWEVER...
The DMCA makes it unlawful to decrypt or otherwise violate any copy-protected or encoded media except as prescribed by the owner. This supercedes Fair use in many cases. So if you're playing a NES rom, technically you are bypassing the rom's copy protection to do so, meaning you may be in violation of DMCA. This also applies to using a BIOS, but NOT to reverse-engineered emulated hardware because that is developed from scratch.
Prosecution and Enforcement of the Rights of Developers
Emulation is notoriously hard to regulate, and historically developers have shown little interest in doing so. You as a gamer are almost totally unlikely to be the target of legal action.
Many emulation sites have been in existence for years, some for over a decade, and typically any dispute between distributors and site owners is settled agreeably with cease-and-desist letters or informal requests. By keeping things gentlemanly, the community and developers can coexist without fans suffering. It's a stark contrast to the music or film industry. Of course, NEW titles are defended with much greater zeal as they are still in the market and their emulation is seen to represent lost profits.
There are no laws explicitly barring emulation. The DMCA is not a law, but a set of guidelines for legally actionable behavior. If you are suspected of emulation, then developers and their legal representatives have the following rights in pursuing you:
-They can request access to your ISPs records of your activity, provided at the ISP's discretion
-They can request a court order to examine the contents of your hard drives and other storage if there is compelling reason to believe you are infringing on their rights
-They can take legal action against you for a financial settlement
It would be possible, but almost impossibly hard, to press real criminal charges for emulation, and in most cases a civil interaction with the developer and acquiescence to their (reasonable) requests for cessation should avoid any nasty court experiences. There is even evidence that some developers are emulation-friendly; the ROM for Star Fox 2 was leaked when the game was permanently canceled, developers included emulation instructions on many Dreamcast games, and Sonic Dev Yuji Naka is a notorious fan of emulation, as seen here http://www.theatlantic.com/technology/archive/2014/07/a-quest-to-find-the-secret-origins-of-lost-video-game-levels/373925/
What the Fuck Does This Actually Mean?
Simply this. First, the greatest legal risk is attached to the following games:
-Anything out now
-Anything currently rereleased in a form identical to its original release
-Anything no longer current but which you could reasonably be expected to obtain (such as PS2 games)
The following are safer to emulate but you may be bound by the constraints of software licensure except where protected by Fair Use, and DMCA may apply:
-Any commercial game old enough that it cannot be found in its original form, or ported in a like fashion to a new platform
-Any game requiring a bios to play
The following games are 100% safe to play:
-Games originally released without any legal restriction (freeware or public domain) so long as your method of playing does not violate DMCA
-Games produced illegally and thus lacking in defensibility (bootlegs/unlicensed games)
-Games old enough for fair use that do not require decryption or copy protection circumvention to run
-Games for which there is no current publisher or right-holder (abandonware)