There are some you can disable using the unity-tweak-tool.
sudo apt-get update
sudo apt-get install unity-tweak-tool
Click on Launcher (in the Unity section) and in the Launcher tab:
- set Auto-hide to
- set Urgent animation to
- set Launch animation to
- set Icon backgrounds to
In the Search tab:
- set Background blur to
Click on the Overview button at the top to go back to the main menu.
Click on General (in the Window Manager section). In the General tab:
- set Desktop magnification to
- set Texture quality to
- set Window Animations to
Additionally, you can turn off more animations in ccsm.
sudo apt-get install compizconfig-settings-manager
In the effects category, untick all of the boxes.
In the accessibility tab, untick all of the boxes.
There are probably more you could disable in compiz as well.