Brandon Stark actually, or accidentally, kills Littlefinger instead of letting him off. Brandon will get killed by the Mad King anyways, so Catelyn will still marry Eddard Stark, without all the "you killed my friend" stuff lying around to prevent it from going off without a hitch. So, while Robert's reign will not be quite so prosperous without Littlefinger there to make gold out of nothing, Littlefinger's plots (which are FAR more expansive than the series has let on so far) will not come to pass. (Though it will likely lead to civil war anyways, since Robert finding out about Jamie and Cersei will from Jon Arryn will undoubtedly lead to him killing one or both, which in turn will provoke Tywin to war. Robert will, however, have a legitimate grievance against the Lannisters, and thus Highgarden is unlikely to go against him (especially if Dorne can then take the opportunity to crush them between themselves and the Stormlands)).