The best answer to this question is almost certainly the
PAQ family of algorithms designed by Matt Mahoney. He used it to win several data compression contents, and when I last checked it still held some many of its records. It takes a very long time to compress and can require huge amounts of RAM, but I've seen it significantly shrink even files that were already highly compressed (like existing archives).
You can get the latest version, and all major previous versions (some with different areas of focus, like ease of use or parallel operation), of the command-line utility here: http://mattmahoney.net/dc/zpaq.html
There are also other implementations that you might prefer. If you want a graphical interface, there is an "additional formats" plugin for PeaZip that includes
lrzip is a command-line utility that is optimized for huge (GB-range) files. It uses a long-range redundancy reduction algorithm followed by a second algorithm seleced by the user, which can include a version of the
PAQ algorithm (or various faster algorithms, if you want them). It also has other interesting features, including the ability to use virtual RAM to compress files larger than your system's physical RAM at the expense of slowing down drastically.
In addition to using a powerful compression algorithm, you can reduce the size of your final archive by pre-processing the files with other tools. You can convert some files from inherently bloated formats to leaner ones or strip metadata from them. Using a utility like
dar (though most people here probably prefer the older
tar) you can combine large numbers of files to make compression more efficient, and control the amount of filesystem metadata (like Unix permissions) that programs like 7zip unconditionally add to their archives. Any of these techniques assume that you are willing to commit more personal time in addition to machine resources.
EDIT: I have found that
dar do not allow control over metadata, nor does
tar's feature set as its mission implies. However they both support sparse files and
dar might make compression more efficient if the option to write file headers only in the index is used (normally
tar-style headers in addition to the index).
Regarding GPU compression, I haven't seen that either. It might not be viable if compression is more reliant on RAM than number of cores, like Litecoin.
All programs listed here are free, open-source, and (with the possible exception of
lrzip) available for all major operating systems.