We present the results of a search for neutrino point sources using the IceCube data collected between 2008 April and 2011 May with three partially completed configurations of the detector: the 40-, 59-, and 79-string configurations. The live-time of this data set is 1040 days. An unbinned maximum likelihood ratio test was used to search for an excess of neutrinos above the atmospheric background at any given direction in the sky. By adding two more years of data with improved event selection and reconstruction techniques, the sensitivity was improved by a factor of 3.5 or more with respect to the previously published results obtained with the 40-string configuration of IceCube. We performed an all-sky survey and a dedicated search using a catalog of a priori selected objects observed by other telescopes. In both searches, the data are compatible with the background-only hypothesis. In the absence of evidence for a signal, we set upper limits on the flux of muon neutrinos. For an E-2 neutrino spectrum, the observed limits are (0.9-5) x 10(-12) TeV-1 cm(-2) s(-1) for energies between 1 TeV and 1 PeV in the northern sky and (0.9-23.2) x 10(-12) TeV-1 cm(-2) s(-1) for energies between 10(2) TeV and 10(2) PeV in the southern sky. We also report upper limits for neutrino emission from groups of sources that were selected according to theoretical models or observational parameters and analyzed with a stacking approach. Some of the limits presented already reach the level necessary to quantitatively test current models of neutrino emission.