As silicon is the basis of conventional electronics, so strontium titanate (SrTiO₃) is the foundation of the emerging field of oxide electronics. SrTiO₃ is the preferred template for the creation of exotic, two-dimensional (2D) phases of electron matter at oxide interfaces that have metal-insulator transitions, superconductivity or large negative magnetoresistance. However, the physical nature of the electronic structure underlying these 2D electron gases (2DEGs), which is crucial to understanding their remarkable properties, remains elusive. Here we show, using angle-resolved photoemission spectroscopy, that there is a highly metallic universal 2DEG at the vacuum-cleaved surface of SrTiO₃ (including the non-doped insulating material) independently of bulk carrier densities over more than seven decades. This 2DEG is confined within a region of about five unit cells and has a sheet carrier density of ~0.33 electrons per square lattice parameter. The electronic structure consists of multiple subbands of heavy and light electrons. The similarity of this 2DEG to those reported in SrTiO₃-based heterostructures and field-effect transistors suggests that different forms of electron confinement at the surface of SrTiO₃ lead to essentially the same 2DEG. Our discovery provides a model system for the study of the electronic structure of 2DEGs in SrTiO₃-based devices and a novel means of generating 2DEGs at the surfaces of transition-metal oxides.