The flexural rigidity of single microtubules is measured using optical tweezers. Two new methods are presented. In both the optical forces of the laser trap are used to directly manipulate microtubules grown off the ends of Chlamydomonas axonemes. The shapes of the microtubules are observed by video microscopy as the hydrodynamic forces of viscous flow counteract the elastic restoring forces when the microtubules are moved actively relative to the surrounding buffer medium. To determine the flexural rigidity, the bending of a microtubule is analyzed under a given velocity distribution along its length. Microtubules incubated with taxol after polymerization are measured to be more flexible than those without taxol added. On the other hand, MAPs are shown to increase microtubule stiffness.