German bond yields went to negative recently, ECB made same move, US bonds may follow soon. What it indicates for the world economy?

A long term view covering past 25 years to the projected next one or two decades show a grim future.

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10 year Treasury yields of German bonds

Negative interest rates show desperation. They signal change in the usual norms of central banks. They punish the major banks to maintain high cash levels with them and force them to extend loans to businesses and to weaker lenders. 

In June 2014, ECB became to first major central bank to venture into sub zero interest rate. It means the ECB will charge banks 0.3 banks to hold cash with them for a day. By mid-November in that year, about a third of the government debt instruments issued by Eurozone governments had negative bond yields. It meant that people depositing money with the bank would not even get the principal in full when taking the deposit out. Smaller banks resisted out of fear of losing customers, but complied to a considerable extent.

On the most basic level, Bunds, like Treasuries, are essentially a cash IOU(I owe You) from the government that needs to be paid back in a certain timespan. Since government bonds from solid countries like Germany are all but certain to be paid back, investors snap them up when they're concerned the economy will be sluggish and don't see any better investment opportunities.