We investigate quantum transport phenomena in multiwall carbon nanotubes in perpendicular and parallel magnetic field. An efficient gating technique allows for a considerable tuning of the nanotube doping level. We show that the weak localization is strongly suppressed at peaks at certain gate voltages which can be linked with the bottoms of one-dimensional electronic subbands. In large parallel magnetic field, we observe a superposition of h/2e-periodic Altshuler-Aronov-Spivak oscillations and an additional h/e-periodic contribution, which we attribute to the magnetic field dependence of the band structure.