The recent banking crisis and the Madoff fraud taught everyone to be cautious. Some people might want to put a significant part of their portfolio into very safe investments. Even the more risk-loving investors usually prefer to have some riskless assets.
Money market is the most short-term and the most liquid type of investment you can find. It is also one of the safest; only FDIC insured bank accounts and US Treasury bills are safer than money markets. Since money markets were invented in early 1970s, only a couple funds ever lost investor money, and even then it was a loss of just 2-3 cents on the dollar.
Due to the slew of bank failures occurring at that time, the U.S. Department of Treasury temporarily protected money market investments as of September 18, 2008. This is not going to help you if you invest today, since the protection only applies to holdings as of September 18, 2008, but at least it helps money market funds avoid any problem of a bank run. Note that money market funds are not, and never have been, FDIC insured. However, a money market account at a bank is always FDIC insured, along with any other bank account.