What file compression application is the most space-efficient?

I have a bunch of directories that I want to keep, but I also want to clear out storage on my drive.

What is the most efficient (in terms of compression ratio) compression application? I don't care if it's slow as I will not be accessing these files often.

The only constraint is that the program must run on OS X.

the program must run on OS X

I'd say your best bet would be any one of the 7-Zip derivatives for Mac OS X.

7-Zip is free open source software and the compression ratio is marginally better than Rar.

StuffIt also does compress very efficient, however, the price of $80 is rather steep, for that money you'll get a 1 TB hard disk. :)

What file compression application is the most space-efficient?

Here's an extensive test comparing about 250 different archiving programs (not all of them available for Mac OS X though) in various scenarios:

Lossless data compression software benchmarks / comparisons

The storage ratio depends entirely on the data you're compressing. Different algorithms have wildly differing performance.