First I made a folder in dropbox for my game saves and made a copy of my current saves out there.
Next I removed the contents of the zsnes folder located at
/home/
Steps:
(Make sure you've saved the files from .zsnes folder below first
cd ~/.zsnes
rm * (this gets rid of the files)
cd ..
rmdir .zsnes
Finally I setup a simlink from my dropbox to the folder so I always had my game saves synced.
Steps:
cd /home/
ln -s ~/Dropbox/zsnes .zsnes
Substitute the path with your path and bam you're done!
Good luck