In your applications, you might have to deal with compressed files: ISO images of installers, e-book or e-comic types based on ZIP files, video DVD images.
libarchive makes things easier by allowing you not to have to deal with external commands to extract those few files you care about.
The API feels a bit antiquated, compared to using GLib/GIO for files handling, but it's generally easier than dealing with potential security issues launching external tools, or even dealing with shell argv quoting.
totem-pl-parser uses libarchive to determine what type of video disc image are hidden inside an ISO image.
gnome-epub-thumbnailer (as well as its siblings, the Krita and OpenRaster thumbnailers I talked about more recently) uses the ZIP handling to extract particular files, and figure out which file is the cover image.
Other uses and limitations
Boxes could use libarchive to extract files from ISO images for its auto-installer, evince could use it to handle CBZ e-comics.
There's a couple of limitations though. ISO support doesn't handle UDF images (which just means weird filenames, not inaccessible files), and RAR support is still quite young.
I hope that this post can spur on bug fixes for the RAR support, new UDF support, or even a GIO-style wrapper around the library.
The upstream authors have been particularly good at fixing bugs that only showed themselves with broken files, and I'd like to thank them for their very useful work.