One interesting kind of dimensionality that is present in all literature is the dimensionality of narrative: how the story is organized, how all its components fit together and how it all plays out.
All good stories are multidimensional, incorporating the elements of character, plot, theme, metaphor, and so forth, into their greater (hopefully) whole. Some stories, though, are told in such an unusual way that they can be regarded as higher-dimensional.
Quentin Tarantino, a popular contemporary American filmmaker, plays with narrative structure in his movies (which include "Reservoir Dogs" [1992] and Pulp Fiction [1994]). Tarantino eschews chronological storytelling, opting instead for a mosaic approach. A typical Tarantino editorial framework would involve starting at one of the movie's two or three climactic moments, flashing back to give character and plot background, flashing forward to another high-tension area involving a separate but related subplot, flashing back to another time to reveal the connections between the two plots, and finally flashing forward to the ending climax.
Why does this approach make for such exciting cinema? For one thing, it engages the viewers' minds, since they have to work harder to follow the action. Tarantino's movies are immensely entertaining on a bit-by-bit level, because they are cleverly written and well-acted, but they are fundamentally satisfying because each little bit fits perfectly into the whole.
Tarantino's work is striking because we usually only see this type of narrative technique in novels, where it is not considered unusual for there to be multiple narrators or flashbacks. Movies tend to be much more chronological and straightforward in their storytelling style. But the success of Pulp Fiction will probably engender a wave of movies which are braver about jumping around in space and in time.
Movies are already multidimensional, because they combine story, acting, editing, lighting, and all those other Academy-Award categories into a coherent whole. Books can be just as complex narratively, but a novel, while it can (and probably does) contain as many or more Ideas as a film, does not have to integrate as many components in order to tell its story. Most movies operate as if they were one- or two-dimensional: they focus on story, on action, or at the most on acting and dialogue. Since movies are such an inherently multidimensional art form, it's encouraging to see directors like Tarantino take advantage of this, rather than ignoring it or trying to work around it.