General:
* Unity
* Camaraderie
* Solidarity
* Cohesion
* Fellowship
* Harmony
* Closeness
* Bonding
* Connection
* Accord
More specific:
* For family: Kinship, familial bond
* For friends: Companionship, comradery
* For a community: Collective spirit, community spirit
* For a group working together: Collaboration, synergy, teamwork
* For a sense of being connected to something larger: Belonging, shared experience
The best synonym for "togetherness" will depend on the specific context and the nuance you are trying to convey.