Construction and commissioning of the cubic-kilometer IceCube neutrino detector and its low energy extension DeepCore have been completed. The instrument detects neutrinos over a wide energy range: from 10 GeV atmospheric neutrinos to 1010 GeV cosmogenic neutrinos. We will discuss initial results based on a subsample of the more than 300,000 neutrino events recorded during construction. We will emphasize the measurement of the high-energy atmospheric neutrino spectrum, the search for the still enigmatic sources of the Galactic and extragalactic cosmic rays, and for the particle nature of dark matter. We will also discuss the first observation of PeV-energy neutrinos.