That is essentially what might happen in the US. A new bill is being proposed that would prevent the public from having access to research that was publicly funded. If you wanted to see that research you would have to pay to see it, meaning you would have to pay for it a second time. Not only does it mean you aren’t getting what you pay for but it prevents the public from having an ability to interact with science and see how it works. That is detrimental to the understanding of science and is problematic for any institution that doesn’t have the funds available to pay for access to important work.
Still in science, the National Science Advisory Board for Biosecurity (NSABB) has been trying to censor research. The research in question centres around the H5N1 flu virus which has been altered to make it easily-transmittable between ferrets in order to understand what mutations could cause it to become a pandemic in humans. The NSABB has asked for the details of how the research was carried out to be kept secret and only revealed on request and after the scientists wanting the information have been vetted. This has received a lot of attention as this is completely against the philosophy of science, which thrives on openness and availability of ideas. There are risks of the wrong people getting their hands on that sort of information but we can’t constantly hide anything beneficial on the off chance that someone could use it for evil.
Outside of the science field, there is also the attempt to pass SOPA/PIPA, two bills that are meant to protect intellectual property online but which are poorly worded and can easily result in vast swathes of the web being shut down for no reason. the bills originally received some support from tech companies, although the main force behind them is the entertainment industry, but now technology companies are strongly opposed to the bills. An open letter in opposition to the bill has been signed by 83 people who were involved in the design and specifications of the internet and many large internet corporations, including Wikipedia, Google, Mozilla (makers of Firefox), Yahoo! and Facebook, have all threatened to take their sites offline, for one day, in protest.