General:
* Humidity
* Dampness
* Wetness
* Dew
* Water (in some contexts)
More specific:
* Hydration (referring to the state of being hydrated)
* Liquor (referring to a liquid substance)
* Humidification (referring to the process of adding moisture)
The best synonym depends on the specific meaning you want to convey. For example, "humidity" is a good synonym for "moisture" in the air, while "dampness" is more appropriate for describing a surface that is slightly wet.