We present results on searches for point-like sources of neutrinos using four years of IceCube data, including the first year of data from the completed 86 string detector. The total livetime of the combined data set is 1373 days. For an E⁻² spectrum, the observed 90% C.L. flux upper limits are ~10⁻¹² TeV⁻¹ cm⁻² s⁻¹ for energies between 1 TeV and 1 PeV in the northern sky and ~10⁻¹¹ TeV⁻¹ cm⁻² s⁻¹ for energies between 100 TeV and 100 PeV in the southern sky. This represents a 40% improvement compared to previous publications, resulting from both the additional year of data and the introduction of improved reconstructions. In addition, we present the first results from an all-sky search for extended sources of neutrinos. We update the results of searches for neutrino emission from stacked catalogs of sources and test five new catalogs; two of Galactic supernova remnants and three of active galactic nuclei. In all cases, the data are compatible with the background-only hypothesis, and upper limits on the flux of muon neutrinos are reported for the sources considered.