Take a look at Libarchive. I spent a lot of time seeking for a cross-platform and LGPL licensed library with convenient interface. This the best of all I've seen. Very easy and powerful tool. Originally designed for Unix-like systems but there's also the Windows version.
I've had great results with miniz: https://code.google.com/p/miniz/
For a simple compression of strings in c++, I also really like Timo Bingmann's solution.
I'd recommend ZipLib https://bitbucket.org/wbenny/ziplib/wiki/Home
Personal reasons why I love this project:
It took me a long time to find this project - hope this helps someone.
We've used zlib a couple times here. It's a fairly standard library that has implementations in most main languages.
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