I've been using PROPACK lately to perform SVD on a gigantic matrix, and it kicks ass. It's a fortran and/or MATLAB package for SVD of large sparse or "structured" matrices. http://soi.stanford.edu/~rmunk/PROPACK/

You just have to provide a matrix-vector product function, specify a few parameters (how many singular values to find, should it compute the singular vectors, maximum number of iterations, etc) and it takes care of the rest. It uses the Lanczos iteration approach mentioned in sibling comments, and it seems like a far nicer implementation than SVDPACK and SVDLIBC.

Let me know if you want a copy of my C interface to PROPACK.