Because of QE, the money supply has increased substantially since 2008. Why aren't we seeing more inflation?
As noted, the Federal Reserve has significantly expanded its balance sheet from about $800 billion prior to the Financial Crisis, to roughly $4.5 trillion as of November, 2014. The Fed expanded its balance sheet by buying long-term assets and securities in an effort to help facilitate an economic recovery, by reducing long-term interest rates, after short-term interest rates had already been driven to zero in 2008. This action is often referred to as quantitative easing (QE). As also noted, however, inflation has remained relatively low despite the various rounds of QE since 2008.
The direct result of QE is an increase in the level of commercial bank reserves that are held at the Fed. It is important to note that this, alone, does not directly lead to an increased circulation of cash in the economy, which could be inflationary. Banks may choose whether to lend funds in excess of required minimums, thereby circulating it into the economy, or simply hold these reserves in their account at the Fed as excess reserves. The indirect effect of QE on the money supply, by fostering additional bank lending, is often debated. However, one of the primary reasons overall inflation has remained low has been because aggregate business and consumer demand for loans, despite historically low long-term rates, has been sluggish. This sluggishness has caused banks to hold significant amounts of excess reserves at the Fed, safely, rather than lend into an economy still recovering from a deep recession and still exposed to underlying risks.