This would be disruptive. DeBeers wouldn't last the day. Economies would collapse. Hellfire would rain down.
Eventually, however, I suspect our complex adaptive world would return to a balance. A new generation of improved replicators would replace the old ones. The new ones would come with controls that made it, for example, impossible to replicate currency. Civilization wants to survive.
We saw this with VCRs. The first recorders were amazing at capturing movies, but later generation devices incorporated "macrovision" copy protection. Recording features became less common, VCRs became largely playback devices. The rebel was subverted.
We're seeing it now with the digital replicators of our era. First generation devices made perfect copies of CDs and even DVDs. Slowly, however, the market is moving from general purpose computers with computers that won't replicate some DRMd video to iPad-style "curated computing". Surprise -- the iPad won't rip a DVD. It won't even rip a CD. (If record companies aren't buying 2nd hand CDs and destroying them they deserve to perish.)
In 20 years, it will be fairly hard to replicate many things. In a world with limited local storage, you may find your purloined media won't survive long in the cloud. The system is strong, It wants to live.
If you think about DRM, a lot of things make sense. Why are Apple so virulently opposed to Flash ? Why is Adobe dissembling when they say Flash is open (they published the specs)? Because the video codecs in Flash are not nearly as important as the DRM (Digital Rights Management) technology in Flash. That is most assuredly not open; it's as closed as Apple's FairPlay. What's Google up to with Google TV and their app stores? Check out the DRM to understand. Why are Hulu and Netflix reluctant to sign on the iPad? Because they'd have to substitute FlashDRM for FairPlay. That means Apple would own them.
This battle will rage for a time, but in 20 years it will be largely forgotten -- and the digital replicators will have been tamed. Resistance is futile.
- Gordon's Notes: The limits to DRM: my new car stereo (in 2007 I was still resisting)
 Personally, like virtually all Mac geeks, I despise Flash and consider Adobe to be as decrepit as Microsoft. I agreed with pretty much everything Jobs wrote about Flash in his open letter. I think, however, that even if none of those things were true Apple would be at war with Adobe. Part of Jobs evil genius is that he's a master magician -- he distracts with one hand while he moves with the other.