Question Ranking
Pros
Pro Free and open source
7-Zip is licensed under GNU LGPL, and the *.7z format has support across all major operating systems. There should be no trouble opening the archives under any operating system, and no need to deal with messages bugging you to register or pay for the app. Source code can be found here.
Pro High compression .7z format
Their own file format .7z that ships with 7-Zip is one of the best compression formats. 7z file format is usually more compact than Zip.
Pro Very fast compression/decompression.
7z is muli-threaded, allowing it to do very fast compression and decompression.
Pro Lightweight
Starts quickly.
Pro Unobtrusive
No nag screen.
Pro Explorer right-click menu integration
Makes it easy to open any archive file, or create new archives, without having to go open another program first.
Cons
Con Does not support data recovery
It's not possible with 7-zip to add data recovery records to the archive which could repair minor integrity errors.