Zopfli is a new data compression algorithm from researchers at Google which seems to work better than most existing compression algorithms out there. The trade off is that it can take much longer to finish compressing files, but more space and transmission time are saved. It is recommended for compress-once-distribute-many-times use cases.

An excellent writeup of how Shamir's Secret Sharing Scheme works. There is even a simple demo linked off of this page. This is also the homepage of SSSS, which is a command line utility that implements SSSS for secrets (up to 128 characters in length).