That is driving economists to speculate about all sorts of scary scenarios, on the assumption that the devaluation trend gets deeper and extends itself to consumer banking rates or countries outside Europe. Like the US.
One obvious side effect of negative rates is that people would withdraw money from their banks and hold cash. That practical problem means that it is very difficult for banks to push a "real" interest rate on consumers past about -0.5%. Once the negative penalty starts to bite, people just hold bank notes that don't cost fees.