Similar to silicon that is the basis of conventional electronics, strontium titanate (SrTiO3) is the bedrock of the emerging field of oxide electronics. SrTiO3 is the preferred template to create exotic two-dimensional (2D) phases of electron matter at oxide interfaces, exhibiting metal-insulator transitions, superconductivity, or large negative magnetoresistance. However, the physical nature of the electronic structure underlying these 2D electron gases (2DEGs) remains elusive, although its determination is crucial to understand their remarkable properties. Here we show, using angle-resolved photoemission spectroscopy (ARPES), that there is a highly metallic universal 2DEG at the vacuum-cleaved surface of SrTiO3, independent of bulk carrier densities over more than seven decades, including the undoped insulating material. This 2DEG is confined within a region of ~5 unit cells with a sheet carrier density of ~0.35 electrons per a^2 (a is the cubic lattice parameter). We unveil a remarkable electronic structure consisting on multiple subbands of heavy and light electrons. The similarity of this 2DEG with 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 route to generate 2DEGs at surfaces of transition-metal oxides.