I have a directory full of
*.avi files. I'd like to compress this directory into an archive of the smallest possible size. What compression software would produce the smallest archive file?
In your case, the most efficient algorithms would be ones designed specifically for audio and video data, since they can discard unneeded data with lossy compression, resulting in far better results than generic algorithms implemented by Zip or 7zip. Examples are MPEG-4, VP8 and Theora for video, MP3, AAC and Vorbis for the audio tracks.
Most AVI files, however, are already compressed using some combination of those or other algorithms. Compressed data doesn't further compress very well, so with 7zip the best you can expect is maybe 1%-3% reduction, no matter what algorithm you choose.
Your only options are to re-apply video compression again – this way you would permanently lose quality – or to buy a bigger hard drive.
Actually you will not have much compression with avi files, however, most of compression programs have a configuration that allows you to set the compression rate when zipping files. Check on 7-zip when you add files to compress it will show you a lot of configurations, one of them is the compression rate.