Zip an archive without including parent directory

Use the -j or --junk-paths option in your zip command.

From the zip man page:

-j

--junk-paths

Store just the name of a saved file (junk the path), and do not store directory 
names. By default, zip will store the full path (relative to the current 
directory).

So if I understand correctly, you are trying to archive the files & folders in a particular folder but without including the root folder.

Example:

/test/test.txt
/test/test2.txt

where test.txt and test2.txt would be stored in the zip, but not /test/

You could cd into the /test/ directory then run something like,

zip -r filename.zip ./*

Which would create an archive in the same folder named filename.zip. Or if running it from outside the folder you could run,

zip -r test.zip test/*

The /* is the part that includes only the contents of the folder, instead of the entire folder.

Edit: OP wanted multiple zips, solution ended up being a bit of a hack, I am curious as to whether there is a better way of doing this.

for d in */ ; do base=$(basename "$d") ; cd $base ; zip -r $base * ; mv "${base}.zip" .. ; cd .. ; done;

How about this command?

$ cd somedir ; zip -r ../zipped.zip . * ; cd ..