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 off
set Urgent animation to No animation
set Launch animation to No animation
set Icon backgrounds to No colouring.
In the Search tab:
set Background blur to off.
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 off
set Texture quality to Fast
set Window Animations to off.
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.