The determination of the alternative splicing isoforms expressed in cancer is fundamental for the development of tumor-specific molecular targets for prognosis and therapy, but it is hindered by the heterogeneity of tumors and the variability across patients. We developed a new computational method, robust to biological and technical variability, which identifies significant transcript isoform changes across multiple samples. We applied this method to more than 4000 samples from the The Cancer Genome Atlas project to obtain novel splicing signatures that are predictive for nine different cancer types, and find a specific signature for basal-like breast tumors involving the tumor-driver CTNND1. Additionally, our method identifies 244 isoform switches, for which the change occurs in the most abundant transcript. Some of these switches occur in known tumor drivers, including PPARG, CCND3, RALGDS, MITF, PRDM1, ABI1 and MYH11, for which the switch implies a change in the protein product. Moreover, some of the switches cannot be described with simple splicing events. Surprisingly, isoform switches are independent of somatic mutations, except for the tumor-suppressor FBLN2 and the oncogene MYH11. Our method reveals novel signatures of cancer in terms of transcript isoforms specifically expressed in tumors, providing novel potential molecular targets for prognosis and therapy. Data and software are available at: http://dx.doi.org/10.6084/m9.figshare.1061917 and https://bitbucket.org/regulatorygenomicsupf/iso-ktsp.