Emulation isn't illegal and it can't really be made illegal.
The Wii has an emulator - how do you think most of those completely-legitimately-licensed C64, Megadrive (Genesis), SNES (Famicom), etc. Virtual Console games work on it?
Atari license their old arcade games with the original ROM's in an emulation package that you can buy on Steam today.
Williams also did the same many years ago (I know, because I have the disk somewhere).
Steam, and GOG.com, also have dozens of titles that are purchased as emulated packages using DOSBox.
You can pick up little £10 consoles that play the original Space Invaders or even 20+ Megadrive games, completely legally licensed, from any big store in the UK.
Some consoles are emulators too - for instance, the SuperGameboy contained chips that "emulated" the original Gameboy but worked on the Super Nintendo. The Playstation 2 had emulation code that ran Playstation 1 games, no matter who made the games (but their emulation wasn't perfect so some things didn't run).
RM used to sell a PC to schools in the UK that emulated the BBC Micro so they could move their old software across.
Amstrad officially allow the use of ZX Spectrum ROM's for emulating that particular machine.
Emulation is an inherent part of computing, even the old mainframes used to perform emulation in their tasks. And it's even been ruled in some countries that if a company deliberately makes it so that you have to infringe copyright/trademarks in order to emulate a title that you legally own, that copyright/trademark is basically void for that interoperability/emulation purpose because some companies tried to make it so that to emulate a device you had to infringe their copyright. It didn't stand up, and people were able to copy whatever was required for interoperability / emulation. This has happened with printer cartridges (that would only be accepted by the printer if they contained a copyrighted set of data), games consoles, large software suites, etc. A similar example: The Nintendo Gameboy had a Nintendo logo that was stored on every game. If the checksum of that graphic didn't match the checksum of the official Nintendo trademarked logo, the Gameboy would not boot the game. This is why sometimes the Gameboy would give you a black rectangle instead of the scrolling Nintendo "ping" each time it was booted up - because for some reason the checksum didn't match that time.).
The only possible thing that emulation can catch on is a software patent (assuming that the emulator hasn't been ripped off from someone else, etc.). Most places in the world don't consider those legal or binding even if they are registered. But a tiny freeware utility can step on a software patent, as well as a million and one other pieces of software. Emulators have a long history, back to the very early days of computers. They have been ruled not illegal many, many, many times.
ROM's, however, are nothing more than programs that run on a different processor to your PC. Copying them if you don't officially have a license to use that software is exactly the same as copying Microsoft Office without a license. Some ROM sites put about rubbish about there being a "24-hour rule". It's a lie, there isn't a country in the world that has such rules. Treat ROM's like you would licensed software - if you found a link to hundreds of full versions of Office, Windows, etc. on a site that wasn't Microsoft's and wasn't asking for payment, that's just the same to download as a ROM that you don't have a license for.
The question of other licenses (e.g. if you bought a copy of the Atari game from Steam or own the original arcade cabinet, can you use those ROM's outside the program, or use other ROM's from the Internet for the same game, or even use those ROM's outside of the original device at all etc.) is much, much more dubious and there is no real definitive answer. It's likely that nobody would care if you could produce *some* sort of license but that is in no way legal advice. StarROMs used to sell officially licensed Atari arcade games online but they apparently went out of business. Some arcade / console game manufacturers have relicensed some/all of their ROM's to "freeware for non-commercial use". There's half a dozen of so legal MAME ROM's like that, a few hundred ZX Spectrum games, etc.
Emulation is completely 100% legal, provided that the code itself wasn't made by copyright infringement (e.g. stealing the console manufacturer's devkits, stealing someone else's code, etc.). MAME has never had any legal problems whatsoever, because the manufacturers of the many thousands of machines it emulates know that emulation is legal. The same for MESS and all those console manufacturers. You can even sell emulators that you've made yourself for profit: Nintendo do it with their Virtual Console titles, and I own several completely legitimate paid-for emulators that use licensed technology (Spectaculator and Gerton Lunter's Z80, that between them contain licenses for the ROM code in the Currah Microspeech, the ZX Spectrum ROM's, Romantic Robot's Multiface ROM, Disciple disk interface etc.).
Emulation is fine. A ROM, though, is just like any other game. If you didn't pay for it, and the license says it's copyrighted, and it's not been relicensed as freeware or otherwise, then you can't legally play it. It doesn't matter if it's "just for 24 hours", if the manufacturer went bust 20 years ago, or because you own a similar game on another device.