I choose rar because you can split big file size into separate part and without rar just forget about downloading file from rapidshare because all file in rar format.
used to work with zip untill rar came along. now i do prefer rar and it can have a password too this adds more to security so i like it more
I use winrar, but for compressing files that I'll be sending to people or hosting I usually use the zip format.
I like winrar because it handles tarred/gzipped files. I'm not sure if winzip does these days. I use tar/gzip to back my data up and using winrar makes it easy to recover incremental backups. I just select from the first incremental up to the date where I want to recover and hit extract.
The only choice is 7-zip. It can compress to zip, rar, 7z and several other options. Additionally it is open source and completely free so you do not have to deal with all the licensing and registration stuff in WinZip and WinRAR. As for the actual compression format, I usually use .zip just because of the widespread compatability.
I prefer RAR. It can compress better than Zip, its secure also. Most of the files I download from the net are compressed by WinRar and are in RAR format. So I prefer RAR.