^{Tested in Ubuntu 14.04}

Those bookmarks are controlled by ~/.config/user-dirs.dirs and commenting out a lines configures the appearance of the list

As an example, to remove the Videos bookmark from the list change the line:

XDG_VIDEOS_DIR="$HOME/Videos"

to

#XDG_VIDEOS_DIR="$HOME/Videos"

Note:

After login the file ~/.config/user-dirs.dirs gets reverted to the original set by /etc/xdg/user-dirs.defaults. To prevent that make the file "read-only" either by right clicking and then properties > permissions or using the command

chmod -w ~/.config/user-dirs.dirs

If you need to edit the file again do the opposite via Nautilus or use the command

chmod +w ~/.config/user-dirs.dirs

If you want to apply this to all users in your system change the file vim /etc/xdg/user-dirs.conf and set the option enabled to False. You need root permissions or this.