So backups are against the law in the UK? How does that work?

Note: You can digitally "rip" an audio CD as a digital file; technically you are making a backup of the data that forms the audio on the CD. Provided you are only doing this for your personal use (not sharing), and you keep the original (that's an important part) - I can't see how such a law would even be enforceable?

Furthermore - what if you have old software from say, an IBM/370 system - that your business needs? You don't have that system any longer because the pieces all died, and they went to a museum, but you still rely on the software written in COBOL, so you run it on an emulator on a PC...

...obviously, the software is no longer running off of tapes or punchcards or whatever - ie "format shifting" - does this law cover that scenario too? "Sorry, chap, you'll just have to stuff your business because your antique computer died, but them's the breaks, mate?" - my sincere apologies... :)

Seriously, though - it just seems a trifle limiting if that's the case - ultimately preventing the use of backups and shifting of those backups onto future media (can you copy a floppy to your hard drive and run it from there?)...

Here in the United States, backups are allowed, of any media; but I do think there is a technical limitation in that you have to own the original copy, and you have to make the backup yourself. Thus, a copy of a ROM for an emulator would be a-ok, as long as you own the original cartridge, plus the original system it runs on - but you have to pull that ROM image from the cartridge (and any images needed for the emulated system from the original system) yourself - a copy from another source is not "legal".

In practice, nobody does this, though - but it probably could be checked for via serial numbers in the ROMs, if they wanted to enforce it.

IIRC/IANAL/etc, in the US backups in and of themselves are not infringement, but transferring tools that break copyright protection is illegal. So, you can back up your DVD, but you can't transfer (upload, download, etc) tools that break the encryption. So, unless you broke the encryption yourself independently, you're still not in the clear.

The IBM/370 system example seems pretty farfetched. Especially since they said format shifting was a civil thing, not criminal.

In general, there aren't a lot of clear cut laws that state "you can do X, but not Y". Mostly because that's just not how our legal system works. Most of the time, it's more about your intent rather than what you technically did.

The most clear example of this is the differences between first degree murder, second degree murder, and manslaughter. All different crimes with different punishments, but ultimately you technically killed someone.

Another more relevant example is how cybercrimes are treated. Just because a system let you have access to a file does not mean that it was legal access. Otherwise, none of them would be enforceable since it's always a machine granting you access (that you shouldn't have). It's all about your intent.

Usually, if you really are just making your own backups from your own copies, you don't have much to worry about since, at least for now, it's not really enforceable.

You can make backups. Ripping to mp3 to back something up is probably allowed. But most people ripping to mp3 are not backing up their CDs, they're format-shifting, and format-shifting is currently not allowed.