In hopes of clarifying what the Fed has done—how it has expanded its balance sheet, and what that means—I offer the following chart:
The blue bars represent the Fed's balance sheet in January 2007, well before the financial crisis of 2008 erupted and Quantitative Easing began. The red bars represent the Fed's latest statement of its balance sheet, which can be found here. I've simplified things considerably (e.g., I've not included reverse repo agreements and other miscellaneous liabilities), but the story remains the same.
The left portion of the chart represents the Fed's liabilities, while the right side represents the Fed's assets. At the end of the day, the Fed's purchases of notes and bonds were offset by an increase in the Fed's liabilities, most of which are bank reserves (and the majority of those are considered to be excess reserves) and the rest currency in circulation. The Fed effectively transmogrified most of the notes and bonds it purchased into reserves (which are functionally equivalent to T-bills, since they are default free, short-term in nature, and pay a floating interest rate). The banking system has been happy to hold those reserves; rather than lending out the flood of savings deposits (almost $4 trillion since late 2008), banks have preferred to lend the money to the Fed in exchange for reserves.
Note: The increase in currency since 2007 was not "printing money" in the way that Argentina has freely printed money. In the U.S., unlike in Argentina, currency in circulation represents cash that the public wants to hold. In Argentina, the central bank prints up lots of currency which it then "lends" to the government in order to pay bills and benefits. Newly printed cash floods the economy—nobody wants to hold all that extra cash—and pushes up prices in the classic inflation definition of "too much money chasing too few goods."
Also of note is that the majority of U.S. currency in circulation is held outside the U.S. by people who actually want to hold it. If the world did not want all that currency, it would be returned to the banking system in exchange for short-term deposits.