I do this all the time - and WinRar does the job just fine.
Select all the files you want to zip, right click (assuming you have winrar shell integration, which is the default).
Select "Add to archive..." to bring up the options.
Select Archive format to "Zip" if you want that instead of RAR
Click on the "Files" tab, and then tick the checkbox "Put each file to seperate archive"
Hit Go, and you are done, every file zipped into to its own archive, named after the filename.zip.
NB This works for whole directories too, so you can move whole dirs into their own archive.