The dynamic responses of a spar, tension leg platform (TLP), and two semisubmersible floating wind turbines (FWTs) in selected misaligned wind and wave conditions are investigated using numerical simulation with an aero-hydro-servo-elastic computational tool. For a range of representative operational conditions, the platform motions and short-term fatigue damage in the tower base and tower top are examined. Although some misalignment conditions result in increased motions both parallel and perpendicular to the wave direction, aligned wind and waves cause the largest short-term tower base fatigue damage for the studied platforms and conditions. Several factors which lead to larger fatigue damage for certain platforms in particular conditions are identified, such as tower resonance due to the 3p blade passing frequency in low wind speeds; surge and pitch motions, particularly in the wave frequency range; and the variations in first-order hydrodynamic loads due to wave direction. A semisubmersible platform with large displacement suffers the least damage at the base of the tower.