Reduce the overall levels. The audibility of harmonics reduces as they increase in frequency, eventually reaching a point where they are inaudible, although they may still be detected by a spectral analysis device. Therefore, reducing the levels of the amplifier will effectively reduce the number of harmonics that are audible. Of course this solution is not suitable in all situations, such as concerts, but can be a useful "quick fix" occasionally, such as in recording.
Reduce the amount of drive/distortion. This will have the same benefits and pitfalls as reducing the overall levels, and may not be suitable for all situations.
Use an amplifier with a type A output circuit. Type A output circuits produce even harmonics, as opposed to type AB circuits, which produce odd harmonics. Again, the application of this method depends on the reason for wanting to reduce the odd harmonics in the first place. If the desired effect is reduced distortion overall, this step will simply replace one kind with another. However, even harmonics are often described as being closer to no distortion at all than odd harmonics, so this may represent a step in the right direction.
Use a digital recording method. If the goal is recorded music, note that analog recording methods tend to add odd harmonics to the sound, rather than even harmonics. Some people believe this plays a role in the coveted "analog sound," which is generally regarded as a qualitatively better sound than digital recordings. Although this step will not reduce the harmonics produced by the amp itself, the overall effect will be reduced odd harmonics on the recording.
Use an input attenuator. This will reduce harmonic generation that occurs at the input of the amplifier, for example, through a guitar connected to a guitar amp. An input attenuator will block the harmonics and prevent them passing through to the amplifier itself.
Use a filtered amplifier. A filtered amp is essentially an amplifier with a built-in input attenuator.