We discuss results from simulations of black hole formation in failing core-collapse supernovae performed with the code GR1D, a new open-source Eulerian spherically-symmetric general-relativistic hydrodynamics code. GR1D includes rotation in an approximate way (1.5D), comes with multiple finite-temperature nuclear equations of state (EOS), and treats neutrinos in the post-core-bounce phase via a 3-flavor leakage scheme and a heating prescription. We chose the favored K_0=220 MeV-variant of the Lattimer & Swesty (1990) EOS and present collapse calculations using the progenitor models of Limongi & Chieffi (2006). We show that there is no direct (or ``prompt) black hole formation in the collapse of ordinary massive stars (8 M_Sun ~< M_ZAMS ~< 100 M_Sun) and present first results from black hole formation simulations that include rotation.