Phase pure, epitaxial (101) rutile TiO2 films were grown on (012) sapphire substrates at temperatures between 485 and 725 degrees C using metal-organic molecular beam epitaxy with titanium tetraisopropoxide as the Ti source. Growth modes and rates were investigated as a function of substrate temperature using reflection high-energy electron diffraction, x-ray reflectivity, atomic force microscopy, and transmission electron microscopy. Growth rates were as high as 125 nm/h. The influence of additional oxygen supplied from a rf plasma source was investigated. Without oxygen plasma, the growth rate exhibited reaction and flux-limited regimes and layer-by-layer growth was observed in the initial stages of film growth. With oxygen plasma the growth rate became independent of temperature; films grew initially in step-flow mode and were insulating. The mechanisms for the different growth modes as a function of film thickness, temperature, and presence of oxygen are discussed.