As investors became more cautious last year they moved their money away from U.S. equity funds and into bond funds, a sign that risk-averse investors are thinking twice after getting slammed by the financial meltdown.

On Thursday Morningstar released a report of the estimated mutual fund and exchange-traded fund asset flows for December, revealing that net inflows for mutual funds amounted to $377.4 billion in 2009, with $356 billion of that total going to bond funds.

At the same time the U.S. ETF industry ended last year with $784.9 billion in assets under management, up from $744.7 billion at the end of November, and $533.6 billion at the end of 2008, according to the report authored by Sonya Morris, an associate director of fund analysis at Morningstar.

As quickly as investors ran to bond funds last year, they ran away from U.S. equity funds, which saw an additional $8.1 billion in outflows in December, bringing the full-year total outflow to $25.7 billion.

Despite the fact that domestic equities got slammed last year, U.S. stock ETFs finished the year with $19.6 billion in net inflows in December.

Some of the outflows from U.S. equities went to international-equity funds, which took in $25.5 billion in inflows, but that doesn’t begin to make up for the $70.4 billion in outflows domestic equity products experienced in 2008, signaling that many investors are sitting on the sidelines.

Where did investors put their money last year? The most popular asset class was taxable-bond ETFs boosted by continued interest in Treasury Inflation-Protected Securities and short-duration ETFs.