Keynesian economic principals take the edge off of the bust cycles of unfettered capitalistic free markets, with that said, they do also soften the edge of the boom cycle as well, and it becomes a cat and mouse game as to just how much government involvement reaches the balance between preventing total economic collapse and exponential economic growth after such collapse. It has its ups and its downs, but overall, I believe that Keynesian economics can be a viable option and tool when an economy is in the toilet.
No, Keynesian Economics does not work, because the governments do not actually follow Keynesian principles, even though they claim they do. If the Keynesian theory were really put into practice, governments would cut back during good times, in order to save money so they can spend during bad times. But in real practice, government just spends a lot all the time.