Money market funds are mutual funds. However, they don't invest in stocks -- they invest in U.S. Treasury bills (notes and bonds with less than 13 months until maturity), top-rated commercial paper, bank notes, and other high-quality, short-term debt instruments. (They shouldn't to be confused with money market accounts, or money market deposit accounts, which are FDIC-insured but pay much lower rates on average).
Money market funds attempt to maintain a stable $1.00 per share NAV (net asset value), so their risk exposure is non-existent when compared with stock and bond funds. Money market funds are not insured or guaranteed by the government (or anyone else), but the Securities and Exchange Commission heavily regulates them; they have a number of restrictions on the quality, maturity and diversity of the securities they may invest in.
Though it certainly is a possibility, no retail investor has ever lost money in a money market fund. There has been just one case of a money market fund "breaking-the-buck," or dropping below its $1.00 share price. In 1994 an institutional money fund, Community Bankers U.S. Government Money Market Fund, liquidated at 94 cents a share due to extensive derivatives-related holdings.
While nothing is risk-free, money market funds have had a far better track record than banks in their 25 year history. The savings and loan bailout alone cost taxpayers billions, while the losses from money fund "bailouts" (where the adviser purchased troubled securities in order to prevent a fund from "breaking-the-buck," or deviating from the $1.00 per share NAV) to advisers, not to shareholders, can be counted in the millions. Remember, even with money market funds, return equals risk (a corollary of "there's no free lunch").