Higgs ID at the LHC

We make a complete catalog of extended Higgs sectors involving SU(2)_L doublets and singlets, subject to natural flavor conservation. In each case we present the couplings of a light neutral CP-even Higgs state h in terms of the model parameters, and identify which models are distinguishable in principle based on this information. We also give explicit expressions for the model parameters in terms of h couplings and exhibit the behaviors of the couplings in the limit where the deviations from the Standard Model Higgs couplings are small. Finally we discuss prospects for differentiation of extended Higgs models based on measurements at the LHC and ILC and identify the regions in which these experiments could detect deviations from the SM Higgs predictions.