General need:
* Require
* Want
* Desire
* Demand
* Crave
* Yearn
* Require
* Depend on
Urgent need:
* Urgency
* Necessity
* Imperative
* Must-have
* Essential
* Vital
Lack or deficiency:
* Deficiency
* Lack
* Absence
* Want
* Shortfall
Specific needs:
* Hunger (for food)
* Thirst (for water)
* Fatigue (for sleep)
* Loneliness (for companionship)
* Curiosity (for knowledge)
To provide for a need:
* Supply
* Furnish
* Satisfy
* Fulfill
* Meet
The best synonym to use will depend on the specific context of your sentence.