Is emulation legal?

The emulator itself is generally legal; obtaining the games usually is not. That distinction is the core of the answer and is frequently blurred.

The emulator. An emulator is software replicating another system's hardware behaviour. Writing and distributing one is lawful in principle, and this was tested in the US in Sony v. Connectix and Sony v. Bleem, where courts found emulators developed through legitimate reverse engineering did not infringe copyright. Emulation of hardware is not itself a copyright violation.

The BIOS or firmware. Many systems require a copy of the console's proprietary firmware, which is copyrighted. Distributing it is infringement. Some emulators avoid this with clean-room reimplementations; others require you to supply it yourself.

The games. This is where it goes wrong. A ROM or disc image is a copy of copyrighted software. Downloading one you do not own is copyright infringement in essentially every jurisdiction, regardless of whether the game is out of print, the console is obsolete, or the publisher no longer sells it. None of those facts create a legal right to copy.

The "you can keep it for 24 hours" claim is entirely fictional, as is the idea that owning the cartridge legitimises downloading a copy from elsewhere in most jurisdictions.

Making your own copy — dumping a cartridge or disc you own — sits on firmer ground in some jurisdictions under personal or format-shifting provisions, and on weaker ground in others. The UK has no general private copying exception; one was introduced in 2014 and quashed by the High Court in 2015, so format-shifting even your own media is technically infringing here.

Circumventing copy protection to make that copy is separately unlawful in many jurisdictions.

Why it matters beyond law. Emulation is central to game preservation — a large proportion of games are commercially unavailable, and archives depend on it. That is a genuine public interest argument, and it does not change the current legal position.