We report on ensemble Monte Carlo transport simulations for semiconducting, single-wall, zigzag carbon nanotubes. The basis for the Monte Carlo simulations is provided by electronic structure calculations within the framework of a simple tight-binding model that takes the effect of the tube curvature on the band structure into account. The principal scattering mechanisms considered are due to the electron-phonon interactions involving longitudinal acoustic and optical phonons. Using ensemble Monte Carlo simulations, the steady-state and transient characteristics are explored. The steady-state velocity saturates due to optical-phonon scattering, and negative differential mobility is obtained for large electric fields. The results also show interesting transient phenomena that are caused by the limited phase space of these dynamically one-dimensional structures.