If you want to make something like this yourself, look into the Lerp function, and then look into the math behind "easing" in animation, it's pretty straightforward. (Which I say as a math illiterate person!)

A good example is Terry Davis's "elephant with blue eyes". I think his animation system didn't have any easing.

Another fun one is Another World, a whole game made with a custom vector graphics and animation system.

And, more recently, Flash, based on the same principles.