In CS6 you can simply use the Create Shapes from Vector Layer function in the Layer menu. Otherwise you will have to use copy&paste to insert individual vector paths from AI as masks or shape layer paths. In either case you will lose some stuff - there's simply no way to retain AI specific features fully editable in AE. Therfore you might wanan reconsider your approach and import the artwork as a flat layer, then animating it with deformation effects like the Puppet Tool, Liquify or Mesh Warp.
Make sure that all your elements are on separate layers in Illustrator. Import as a composition retaining layer size then use tools like Puppet Pin or effects like Mesh Warp to distort the boundaries of the layer so thy stretch up and down like rubber.
Animating the actual vector path can be done using the techniques Mylenium suggested but it would be far more difficult and time consuming and you'll loose things like gradient fills and Illustrator effects. As long as you have continuous rasterization turned on you can stretch and bounce one or all of your Illustrator layers to your hearts' content without any worries about pixelization.
Take a alook at this tutorial by Angie Taylor. It shows how she uses Puppet Pin to make bottles dance.
Angie's great! Love her work.... lots of fun....