Paul Krugman has a nice summary of why he thinks Keynesian economics triumphs over classical economics in explaining the current macroeconomic environment in developed economies like the US.
First, he argues that unlike the classical paradigm which sees employment and output as determined by the supply-side (and thereby the current unemployment rates are due to structural issues or workers preferring not to work for various reasons), Keynesian models give importance to the demand-side deficiencies. Simple supply-side models cannot explain either the current high rates of interest nor their persistence for this long period. If we taken into account the demand-side, there is an urgent need to boost aggregate demand with expansionary policies that both utilizes idle workers and leaves people with more money to spend.
Second, the classical theory of interest rates claims that increases in the monetary base, due to higher fiscal deficits and fiscal expansion, leads to spikes in interest rates and inflation, apart from crowding out private spending. However, this line of reasoning has not been able to explain the extended period of disinflation and declining interest rates and bond yields despite the increasing deficits and expanding monetary base.
In simple terms, they come up short when faced with the zero-bound in nominal interest rates and the resultant liquidity trap. Keynesian models would indicate that in such conditions, where banks were flush with funds and were without takers from the private sector (or desired savings exceeded desired investment), government borrowings would not cause interest rates to rise or crowd-out private spending. Further, in such liquidity traps, deflation and not inflation was the greater risk.
Nancy Folbre has this nice summary of the Keynesian stimulus debate. See these critiques of the structural employment debate here and here. Robert Barro's argument against fiscal spending is made out here.