We're always to that what a story needs as vivid, well-rounded characters that live and breathe and seem to have a life off the written page. Without this, we are told, the story will be flat and uninteresting and whet the appetitie as effectively as a five-dollar pizza placed before a man with a sour stomach.
And yet, this is not always the case. Sometimes you want a character to be underdeveloped. It might be better for him to be a cardboard cutout instead of a real person.
I was recently rereading John Mortimer's short story "Rumpole and the Married Lady" when I was struck by how well the character of the young boy trapped in his parents' divorce case worked. He isn't memorable. In fact, he's nearly a complete cipher and we learn very little about him beyond a fondness for toy soldiers and doughnuts. In any writing class you'd expect such a rice-paper thin sketch to be rejected.
And yet, he worked beautifully because of the part he was supposed to play in the story. We weren't supposed to be interested in him. He was supposed to be the McGuffin in his parents' conflict. He was supposed to be a minor irritant to Horace Rumpole as he interviewed the mother about her divorce. His job was to be overlooked and dismissed–until we learn that he is, in reality, the most important character upon which everything else revolves. Had he been written according to prescription, we'd have taken too much notice of him and the revelation would have been spoiled.
Another example is an Agatha Christie play that I once did when in my more larcenous days I was employed as a professional actor. I'd been cast as a butler and had this been any other character I'd have developed all sorts of quirks, traits, and even a history to flesh him out. But on reading the script, I realised that the butler was meant to be a stock character played as a stock character. His job was to be simple enough that the audience could impose their own assumptions and suspicions upon him. And so, a stock character I played him as.
Then there was the film Sky Captain and the World of Tomorrow, where the stars Judd Law and Gwyneth Paltrow were critcised for being two dimensional. Considering that the plot of the movie was about two people who are dragged through a world where wonder upon wonder is heaped upon them, I contend that the problem was that they weren't two dimensional enough. The film didn't work because the audience was distracted from the wonders, which were the real stars of the movie. Indeed, in many pulp science fiction stories that are now so roundly condemned, many were written with this firmly in mind. Where spectacle or plot are king, characters often need to be taken down a peg to avoid overwhelming the story.
None of this is an excuse for not doing your homework and properly developing a character, but it does show that fiction is not character study and too much emphasis on character can actually weaken a story rather than strengthen it. Look at the current incarnation of Doctor Who where so much attention is spent on character that no one can remember the plots at all–even when the show is on the air. Keep in mind that characterisation is only one part of the story and it must be balanced out against the needs of plot. The key is to find the balance and the balance depends on what sort of a story you are telling.