Krugman has a nice, short summary of the empirical evidence supporting Keynesian economic models. His core points, which are supported by Keynesian economic models but not leading alternative macroeconomic theories:
1. Budget deficits don't send interest rates soaring when unemployment is high.
2. Prices are sticky.
3. Monetary policy can move output and employment.
4. Austerity plans cause economic contractions.
5. Fiscal expansions (i.e. stimulus spending) in the 1930s lead to economic expansion.
Naturally, his Keynesian recommendations are basically that the Federal Reserve have an expansionary monetary policy without worrying unduly about inflation, and that Congress and the President devote more money to stimulus spending and stop worrying about the budget deficit.
Notably, cuts in civilian government employment, especially school teachers, have been a major drag on overall employment in the last two years. Government austerity plans in the United States, what Krugman calls "Hoover" style policies, are having a material negative effect on the health of the American economy.