Let´s take a look on Sweden. The Scandinavian country was the first that reduced interest rates below zero. On 2 July 2009 the Riksbanken, the central bank of Sweden, pushed the overnight deposit rate (the interest commercial banks get for depositing money with the central bank overnight) down to −0.25% (wikipedia). On 12 February 2015 they lowered the repo rate (the rate at which a central bank lends short-term money to commercial banks) to –0.10% and reduced the overnight deposit rate to minus 0.85% (wikipedia).
The result: Sweden's economy grew by 4.5% on an annual basis during the fourth quarter of 2015 (businessinsider). That makes Sweden the fastest growing country in the Western world, leaving the sluggish economies of US, UK and the Euro group far behind.
How did it work?
1. Sweden is a small country (about 10 million residents) and depends on exports (iron ore, lumper). The negative interest rates pushed the Swedish Krona lower on the international currency markets (because global investors are losing money there thelocal). The falling Krona made Swedish goods cheaper on the global markets, pushing the exports. The devaluation also made imports more expensive and reduced purchases for foreign goods.
2. Consumers earn less money for their savings accounts and they get cheaper consumer loans. Both trends are encouraging them to spend more.
3. Cheaper loans, more consumer spending & international demand encourage companies to invest more into their businesses.
Conclusion: It seems that negative interest rates can help a small country to overcome a soft patch. They might also work for the Euro group (especially Italy & Spain). But they work just as a short term remedy and not as a cure against structural problems, like taxes & regulations. Btw the US doesn´t need them because the American economy is already solidly growing (driveby).