It's difficult to draw broad conclusions from single experiments, but the 2008/9 global recession definitely supports the Keynesian view. Countries that responded with stimulus grew their economies out of it, and countries that resorted to austerity are still suffering.
It's hard to know for sure, though. You could equally make the argument that Bush's deregulation and tax cuts for the rich successfully grew the economy, until they caused the 2008 crash. We don't really know what the future of the Bush/Obama stimulus will bring, and we've only had 8 years of amazing growth to support it being the right decision. Maybe next year will finally see the 50% crash some folks have been predicting for years now?
There have been three pretty good Keysesian experiments in this country. The first and best example was the Kennedy stimulus (actually passed when Johnson was president) because it was crafted by rock-ribbed Keysenian economics from Harvard (where Kennedy took economics from John Kenneth Galbraith), and passed somewhat intact by Congress. It worked more or less perfectly, with unemployment dropping like a stone and the economy expanding rapidly with no inflation.
The next was Ronald Reagan, believe it or not. Reagan cut taxes and increased spending, and again the economy responded favorably. Now, Supply Siders like to take credit for this, but in the Supply Side world view, there would be no, or at least very small budget deficits. Reagan promised that if his package was passed, the budget would be balanced by 1984, or maybe 1983. Reagan's package was passed, again mostly unmolested by Congress and deficits exploded. That's of course just as you'd expect. You can't taxes and increase spending without increasing deficits at well. The economic growth also tends to be remembered much more favorably that it actually was. The 1980s were actually pretty meh as far as GDP growth.
The Bush II tax cuts weren't really Keyseian because during most of that era we were close to full employment, so there isn't much room for stimulation. They were created with a Supply Side philosophy. Economic growth was pretty meh over all in this era too and the trickle down of rising wages for the middle class didn't happen as promised either.
Next comes Obama. The Obama stimulus was mostly tax cuts, which are pretty weak stimulus, and the stimulus wasn't very big compared to the economy, but seems to have worked pretty well. We got a record number of consecutive months of job growth with no inflation. That's pretty much the target. Economic growth was on the weak side, however.
A contrary example is Greece. They (at the behest of their creditors, mostly Germany) cut spending and raised taxes in order to generate money. But the opposite happened. Taxes went up as a percentage of GDP, but because the GDP shrank the total number of Euros collected went down. In a Keysenian world, they would have stimulated to get the unemployment down, and that would have boosted the GDP.
