We continue our study of the possible production of supernovae and a variety of high-energy transients by black hole formation in massive stars endowed with rotation: the "collapsar model." The black hole may form either promptly, since a successful outgoing shock fails to be launched by the collapsed iron core (collapsar Type I), or, in a mild explosion, by fallback (collapsar Type II). In the latter case, the inner layers of the star initially move outward but lack adequate momentum to eject all the matter exterior to the young neutron star. Over a period of minutes to hours, ~0.1-5 M falls back onto the collapsed remnant, turning it into a black hole and establishing an accretion disk. The accretion rate, ~0.001-0.01 M s^-1, is inadequate to produce a jet mediated by neutrino annihilation but is similar to what has been invoked in magnetohydrodynamic (MHD) models for gamma-ray bursts (GRBs). This fallback is modeled in detail for two 25 M progenitors using two different one-dimensional hydrodynamics codes, one Lagrangian and one Eulerian. The production and consequences of jets are then explored in both sorts of collapsars. Justification is given for assuming that the jet power is a constant times the mass accretion rate, c², and the consequences of = 0.001 and 0.01 are explored. Adopting an initial collimation half-angle of 10°, the opening of the jet as it propagates through the exploding star is strongly influenced not only by the jet's kinetic energy but also by its initial pressure and the stellar structure. Cold jets tend to stay collimated and become even more so, sometimes having an angle of only a few degrees when they reach the surface. Jets having higher internal pressure than the stellar material through which they pass, or less initial collimation, spread out and tend to make energetic, asymmetric supernovae accompanied, in helium stars, by weak GRBs. SN 1998bw may have been such an event, and other events having energies between that of ordinary GRBs and GRB 980425 await discovery. In supergiant stars, shock breakout also produces bright X-ray transients that might be a diagnostic of the model, but even the most powerful jets (equivalent isotropic energy 10⁵⁴ ergs) will not produce a GRB in a red supergiant. For such Type II supernovae the limiting Lorentz factor is Γ ≈ 2. Type II collapsars should be more frequent than Type I and may power the most common form of gamma-ray transient in the universe. However, the GRBs seen by BATSE are, for the most part, too brief to be Type II collapsars. Those are still attributed to prompt black hole formation. Even there though, the diverse energies and time structure reflect chiefly the viewing angle and the variable collimation of the jet inside the star, not a highly variable "central engine." Indeed, collapsar-induced transients may all have a common total energy in the range 10⁵¹-10⁵² ergs.