- Emulators are totally legal, unless they do things that make any software illegal - infringe software patents (which are a stupid idea but still legally enforceable in places), or are made from someone else's code without permission, etc.
- Some ROM's are totally legal. There are MAME ROM's licensed by the original copyright holder and homebrew ROM's that infringe nobody's rights. Hell, the original ZX Spectrum ROM's are licensed by Amstrad for use in emulators specifically - you just can't claim they are yours or sell them commercially without permission.
- Most ROM's that people want, discuss and download are images of commercial, copyrighted games and other software.
In essence, a ROM is no different to a disk image of an Office installation CD, or even an ISO of a PC game. Yes, the game *MIGHT* be freeware, but if not they are still under copyright. Thus most ROM's on the net are 100% illegal because it's not Nintendo, or whoever owns the rights to them, posting them. They are still commercial products (even if no longer sold). It is *illegal* virtually everywhere to copy commercial copyrighted software and distribute to others, and also to download those things from websites, torrents or whatever.
If you have problems with understanding it, just think "Would I be allowed to link to a copy of Microsoft Office with a fake CD key?" If the answer is no for that, then the answer is no for ROM's too. It doesn't even matter if it was Office 2000, or some old game that hasn't been sold in years - it's the same problem. Microsoft would be the original rightsholder and you DON'T have a right to distribute it or obtain it from anyone other than Microsoft-approved resellers.
Linking to such things may not technically be an offence in itself in some special circumstances and legal frameworks, but even in Europe people have been convicted of "incitement to infringe copyright" just by linking to torrents of copyright software on other servers. The law is so uncertain, and will almost certainly err on the side of the copyright holder than some random joe trying to protect his fair-use rights, that without going to court for every single offence, most places just ban the activity because it's just not worth the legal hassle. It may not be illegal to *sell* a card that just-so-happens to decrypt your Sky Movies, or allow you to bypass iTunes DRM, or let you use your PS3 as a generic computer, but for sure you're going to be in court quite quickly and for a long time trying to prove that's the case. Most forum owners can't / don't want that hassle so even discussion that may lead to such links is banned. If nothing else, co-operating with a police investigation is hassle enough for a forum owner that banning such possibilities arising is only a sensible idea.
Basically, if you DO NOT OWN the original rights to a copyrighted work (and you don't, except for things you've created yourself, or where you've bought exclusive rights from the original rightsholders), you can't just go posting it on any website you like and/or enticing people to download it. Similarly, without a valid copyright license to a work, you can't just obtain it from wherever you like and *assume* you have a right to format-shift (i.e. download a title you have a license for but in a format not original licensed - e.g. ROM's of games you own the physical cartridge for) - your copyright licence almost certainly explicitly excludes that and you'd have to fight in court for years with EACH copyright holder to work out if you *are* allowed to do simple things like that. Even buying a game, or a games console, you are only given very limited rights to USE the software and not to go giving it to everyone and his brother. The ROM's burned into an Amiga when you buy it aren't explicitly licensed for use anywhere other than an Amiga. And most games will not run in an Amiga emulator without a copy of the original ROM, which is copyright and NOT explicitly licensed for such use.
Anyone downloading from such sites doesn't actually have a valid license to use that software - if you did, only the original rightsholder (or their authorised resellers) could supply you with that software, not some random site on the Internet. Only the original rightsholder knows if you've licensed their works, and to what extent. Only the original rightsholder can decide to issue you with replacements, repairs, old versions, etc. and it's completely at their discretion within your licensing agreement with them and they can say "No" if they like and you'd have to fight in court to prove you have an entitlement to that.
So anyone running a website with ROM's/games/software on that doesn't have a licence from the original rightsholder is breaking the law (the only exception I can think of is StarROMs that sold legally-licensed Atari ROM's for a while) - no matter how old that software is (Abandonware = 100% illegal), and anyone who uses it - UNLESS THEY ALREADY HAVE THE COPYRIGHT HOLDER'S PERMISSION TO DO EXACTLY WHAT THEY ARE DOING - is almost certainly breaching the terms of their copyright licence and/or illegally copying a copyrighted work. To prove otherwise, you need to go to court.
The people who run Internet forums don't want to defend their users in court over the user's actions. They also don't want to be forced by law to root through all their logs at great expense to identify forums users, or even to have their servers seized while the police do that. If you think that's somehow an imaginary scenario, I suggest you set up your own forum and see how long you survive. Some places on the net escape because of jurisdictional issues, but setting up a UK-based forum, for example, makes you subject to UK law - which does not take kindly to inciting people towards copyright infringement.
If you wouldn't phone Nintendo and tell them what ROM's of theirs you are linking to, you shouldn't be posting it on a forum for your own sake. For the sake of the forum owners sanity and wallet, they won't let you do anything even mildly grey-area in terms of the law. It's just not worth it.
Do you think the local paper would let you advertise a link to a ROM-site within their sponsored adverts? Same thing. They aren't going to be covering your arse in court anyway, and they don't want the hassle of even one solicitor's letter dropping on their doorstep.