I am making an animation in blender than will get extremely large. Just to know the limits for when I'm working, does anyone know the maximum size of an object in blender?
Size is relative. You can have tiny objects cramped into single blender unit or large objects across hundreds of units and both would render the same size on screen.
The scale of the scene is up to you to choose, you don't have to follow the metric units.
To answer the question, the maximum absolute size is 3.402823 × 10^38 blender units, which is a limit of 32bit float.
Just be aware that there might be some computational artifacts with handling small numbers and with objects too far from scene's origin (precision limitations). These might become visible even for objects just 500 units away from origin: