Is there any good zip application for Mac OS X similar to 7-Zip (Windows only) which is free, compatible with many formats, and offers encryption options?
Check out Keka - the free Max OS X file archiver
Another way is to run the command in your Terminal.app:
After the command you will be prompted for a password. Instead of the single files you can specify a folder, too.
I don't know of any more apps that allow you to create archives with many formats. For decrompression there are multiple great apps (The Unarchiver, Stuffit Expander). You can give 7zipX a try, too.
Some paid alternatives: