SVDLIBC's fastest sparse matrix algorithm uses Lanczos, which is still not good enough for large data sets.

Of particular interest to web scale projects would be incremental SVD methods that enable online updates to the SVD. http://www.merl.com/publications/TR2006-059/

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.