You can either use nurb patches or poly edges. The head of the Thing model you looked at was edge modeled (numerouse edge extrusions and stitching). So far I prefer to use extruded poly edges in areas with lots of detail and the standard box modeling for more general shapes.

Nurbs are another matter entirely. I play with them, but I have yet to build a full model with them. check out Anita's WIP with marlon brando for an example of nurbs patch modeling.