General:
* Damp
* Moist
* Muggy
* Sticky
* Heavy
* Oppressive
More formal:
* Saturated
* Waterlogged
Informal:
* Sweltering
* Claustrophobic (referring to the feeling of humidity)
Specific to weather:
* Sultry
* Tropical
The best synonym depends on the specific situation and the desired level of formality.