Family guy is one of my all time favorite animations. it started off as a drawn cartoon, the characters are amazing, here is an image of one of the first concept drawings of the pilot episode. 

The Family guy grew in popularity they developed the characters more. and moved in to creating it on computer. 

 

They started making the animation on programs such as Toon Boom, as they were able to reuse and create the animations easier. this also gives them the opportunity to use less animators and work to i higher standard.