Believers claim the interventions are orchestrated by a secretive, high-level government committee called the President's Working Group on Financial Markets (popularly known as the Plunge Protection Team). It was created shortly after the Crash of 1987; members include the Treasury Secretary and chairmen of the Federal Reserve, Securities and Exchange Commission, and Commodity Futures Trading Commission.
When the stock market is at risk of plunging, it is alleged that this committee will dip into the Treasury Department’s $40-billion (U.S.) Exchange Stabilization Fund to buy S&P 500 index futures and cause spreads to widen between the futures and cash markets for equities. This then gives arbitrageurs a chance to reap risk-free profits by shorting the futures contracts and buying the stocks in the S&P 500 basket.
Some of the most visible conspiracy theorists are at Canadian hedge-fund firm Sprott Asset Management. Their 41-page study, Move Over, Adam Smith: The Visible Hand of Uncle Sam (.pdf), is perhaps the most substantive attempt at offering a proof.
Concerning the recent rally in the stock market, the Sprott team states in its latest Markets at a Glance that they are having “a hard time believing it is a pure coincidence that the stock market rallies on the eve of U.S. mid-term elections where the incumbent party is at risk of defeat.” They suggest that it's politics: according to a report by the chief strategist at Raymond James, “market analysts and traders have noticed a mysterious ‘bid’ in the futures market since the July lows.”
Personally, I can see some intervention occurring should the market crash like in 1987. The motivation would be to prevent it from snowballing into a financial collapse or depression. But I’m not quite convinced yet that it would be anything much more frequent. Nor am I yet cynical enough to think the interventions are influenced by partisan politics.