The basis for a healthy democracy is an informed electorate, and as such fake news whose only goal is to misinform the populace is a threat. This misinformation can also try a person in the court of public opinion, which can be damaging and a very real threat which is shown in 'pizzagate'. However the potential for corruption of filtering fake news is also high, you could crack down on free speech, misinform the public by censoring information, and give unreasonable punishment to those who made an honest and reasonable mistake.
More should instead be done to raise the standards of the media, and separate the likes of entertainment, informative, and actual news. Standards would be based on accuracy, bias (some bias can be expected but becomes stricter for news, compared to informative), how much it informs people about events (local, state, country, and global), and perhaps even its investigators.
Those who do not meet those standards would be more open to libel and slander charges than those who do (securities made to protect those trying to inform the public or investigate events for the news should not be applied to a gossip rag that is trying to misinform the public).
On a separate note public schooling needs to ensure that people are capable of spotting both bias, and fake news. This is especially important as the fake news on the internet (a major source of information) is likely to get more sophisticated, and seem more legitimate in the future.
Fake new is as old as the hills and more needs to be done to stop it.
The question is, are governments qualified to filter the news. It's no big secret that certain governments have been known to put out their own fake news.
Maybe and independent, impartial entity would be a better choice.
Yes, governments throughout the world should follow Germany's example and filter fake news. As we have seen in regards to the "Pizzagate" scandal, fake news can have real consequences that may put the lives of many people in danger. It is important that the public makes its decisions based on fact.
The concept of fake news is in the eye of the beholder. Governments should not censor any speech; regardless of whether they believe the subject is about real or fake news. Fake news is not the real problem; instead low information citizens are the problem. Society must do a better job of developing critical thinking skills so that people know when something is real or fake.
It is dangerous for governments to be censoring free speech. They will start out filtering only things that are untrue, and in the end that will then turn into them filtering things that they don't want the public to hear. The governments should let people sort out what they believe is true.