You can accomplish very basic synchronization via services like Dropbox.
Exit Stickies.
To sync via Dropbox:
ln -s ~/Library/StickiesDatabase ~/Dropbox/StickiesDatabaseor Google Drive:
mv ~/Library/StickiesDatabase ~/Dropbox ln -s ~/Google\ Drive/StickiesDatabase ~/Library/StickiesDatabaseRepeat steps 1 & 2 on your other Mac(s).
This method is effective, but not very robust. Stickies saves all stickies in one file, and blindly updates it whenever you make a change. And file sync services will not merge a single file, but outright replace it (although they will try to avoid losing your data if changes are detected on both machines).
So, this will only work properly if Stickies is closed on other machines when creating, editing or deleting notes.