Is there any type of software in which you can animate the way the .stl object will be printed?
I'm not talking about what the end result looks like. I'm talking about a tool which acts like it's printing the given object as an animation.
I know it somehow depends on your printer but is there anything I can use?
You may wish to consider Craftware for your purposes. It's a free program in beta form that does provide a tool-path animation for printing the layers. It is not so much specific to a printer as it is configurable for your own requirements. The video shows what I believe you are seeking at about the two minute point.
Simplify3D also provides such information, but is not a free program.
The open source slicing engine, Slic3r, also allow for such a preview. The preview is not animated, but you can see the path that your printer will follow for each layer.
To do this, simply upload a model and press the preview button in the lower part of your screen. To select which layer to preview, use the slider on the right of the preview window.
I'm using MatterControl and it has such visualization. User can see synchronized animation which shows how the object is actually printed and user is able to see each path of filament put onto the layer.
It's possible to control starting and ending position so it's possible to precisely visualize each milimiter of filament even between start and end point.
MatterControl also visualizes extrude flow so if user set extrude to 150% or 200% then application shows wider "line".
All of it can be seen in 2D (from top view) and in 3D (perspective view). There is also possible to see overlay (by transparency) and print speed (visualized by color).
MatterControl also shows non-printing moves and retraction points and their hight.
