These are the only packages you need to run compiz with animation effects on 13.04:
apt-get install compiz compiz-plugins compiz-plugins-default compizconfig-settings-manager dconf-tools
All other packages compiz-plugins-extra etc. are just placeholders in 13.04 (empty packages they created to maintain compatibility), see my list of installed packages (some descriptions in italian)
compiz - window manager e compositing manager OpenGL
compiz-core - window manager e compositing manager OpenGL
compiz-dev - window manager e compositing manager OpenGL - file di sviluppo
compiz-gnome - window manager e compositing manager OpenGL - decoratore di finestre GNOME
compiz-plugins-default - window manager e compositing manager OpenGL - plugin predefiniti
compiz-plugins-main-dev - transitional dummy package.
compiz-plugins-extra - transitional dummy package.
compiz-plugins-main - transitional dummy package.
compiz-plugins-main-default - transitional dummy package.
compizconfig-backend-gconf - transitional dummy package.
compizconfig-settings-manager - Compiz configuration settings manager
compiz-plugins - OpenGL window and compositing manager - plugins
You might have a configuration issue preventing from using the effects, there is a complete profile and apt-get scripts available for download here: http://www.istitutomajorana.it/index.php?option=com_content&task=view&id=2154&Itemid=33 (direct download link: http://www.istitutomajorana.it/scarica2/Compiz-Effetti_3D_Ubuntu_13-04.tar.gz) it worked for me.
The result: I have 3d desktop (both cubic and spheric effects), I can paint fire on the screen, but haven't been able to use it as a Windows Close effect, seems to be an effect of this migration of plugins from sub-packages. Also 3d-windows appears to be broken. But you'll still get a great looking desktop!