In the game setup, there's an option for "Quick Combat". That disables all animations during combat, but it conflicts with a lot of mods for various technical reasons, and so many of us never use it.
Also, if you're playing a mod with custom units, animations are often disabled even if the unit model used is one that had animations previously. This happens whenever the new unit has a different Combat Class (i.e., Mounted, Armor, etc.) than the original. In this case, the issue's unavoidable.