I have used zziplib ( http://zziplib.sourceforge.net/ ) in the past. I had no particular difficulty integrating it into my cross platform (windows, Linux, Mac OSX). I simply used a different extension to make it clear this was to be used with my program. So I could rename my *.lvl files to *.zip and open the file with 7zip, winrar, file-roller, etc...
There are many other libraries too:
Zlib - http://zlib.net/ - Doesn't have a file format but does use gzip.
7-zip SDK - http://www.7-zip.org/sdk.html - Supports LZMA, zip, bzip2 and a few others.
Whatever you pick, be careful with licenses. zlib is known for its very liberal license, but some of these might be under the GPL, which depending on how you use it might require source distribution.
You might also want to check out: Compression Libraries For C++