We fabricated field-effect transistors based on individual single- and multi-wall carbon nanotubes and analyzed their performance. Transport through the nanotubes is dominated by holes and, at room temperature, it appears to be diffusive rather than ballistic. By varying the gate voltage, we successfully modulated the conductance of a single-wall device by more than 5 orders of magnitude. Multi-wall nanotubes show typically no gate effect, but structural deformations—in our case a collapsed tube—can make them operate as field-effect transistors.