The reason I use it is because it's open source and there are no terrible nag screens.
One example, which for me is one of the most annoying aspects of using 7zip, is double clicking on an .exe file or .html file or anything in an archive that relies on other files in the archive (dlls, images, data files, whatever): 7zip extracts only the file i double clicked on, ignoring everything else whereas WinRAR extracts all files since chances are if an executable is part of an archive, it'll need the other files in the archive to work too. This means that with 7zip i have to manually unzip the archive somewhere first, usually drag and dropping the top folder in the archive (assuming it has one, many donts) in the desktop or a temp folder, then open that temp folder, run it and then delete the folder. With WinRAR i just double click the executable and WinRAR does the rest. This is very useful when i want to run some game from a gamejam, run an installer which for whatever reason isn't part of an executable, test an archived build of a project that is made up of exe+data, check an archived webpage that is made up of several html and image files, etc.
As a sidenote (and another source of frustration), 7zip also has the annoying behavior of deleting that temp file almost right after it extracts it (i'm not sure exactly how it decides that) which means that unless the associated program is fast enough to open it, it'll get deleted under its feet, creating a race condition between the associated program and 7zip.
There are other issues with 7zip as well as a lack of features (practically zero features in the self-extracting archive generator, as an example). The main reason i have it installed is because it can open more formats than WinRAR, especially useful when dealing with disk images from VirtualBox since i can simply open it with 7zip and extract files from there directly without booting the VM. But when it comes to working with zip, rar and even 7z archives, i stick with WinRAR.
BTW, the "terrible nag screens" go away from WinRAR once you buy it. It has been a while since i saw any of those.
