A regularized singular value decomposition is one of the most powerful machine learning algorithms available. Two decent open source implementations are SciPy (http://www.scipy.org/) and SVDLIBC (http://tedlab.mit.edu/~dr/svdlibc/).
There's also been research in academic circles regarding the use of the much more efficient (though nondeterministic) CUR decomposition in the areas of network analysis and collaborative filtering.
Timely Development also posted the full c++ code they used for the Netflix Prize http://www.timelydevelopment.com/demos/NetflixPrize.aspx