Monsters Inc - Sulley

One character that instantly sprung to mind when it came to limitations is Sulley from Monsters Inc. I thought of this after remembering the staff at Pixar discussing on a documentary how it took the guys 12 hours to render the 2 million plus hairs on his body. Even though Pixar had some of the best computers for animation and 3D wasn't that uncommon then (especially after Toy Story) the detail in Sulley was a big limitation which took the best part of a day to just even render. 

Pixar don't tend to do things by halfs as anyone who's seen any of their animations will know. Their attention to detail is very hard to beat and this has obvoiusly paid off as this has made them iconic.

It may be incredibly hard work to achieve this sort of detail, but I highly doubt Pixar would be half as popular is their animations were 2D.