Animation is everywhere in OS X, and it is not possible to disable all animation with one global setting, which makes this a very complicated question to answer completely.
I would advise you to try disabling things one at a time as you find animations that annoy you. Check System Preferences to start. For example, the Dock magnification animation can be turned off in System Preferences -> Dock.
Also, check out TinkerTool, which allows you to do the following:
- Disable the animation effect when opening files in the Finder
- Disable the animation effect in Mail
- Disable the animation effect in Mission Control
- Disable animation when hiding or showing Dock
- Disable fade-in and fade-out effect,and animation when switching between pages, in Launchpad
- Disable animation in opening windows
- Disable the animation effect when opening information panels or Desktop icons
- Disable the animation effect when selecting information categories
- Accelerate the animation of opening and closing sheets
If there’s an animation that really bugs you and you can’t figure out how to disable it, try posting a separate question here at Ask Different for that specific issue — you will get a fast and accurate response. (And as a nice side effect, both you and the people helping you will earn more rep that way.)