Batman: Batman is the leader and core member of the Batfamily. He has trained the majority of the Batfamily into becoming hero's including his three Robins and Batgirl. He has also successfully reformed villains such as Catwoman and Huntress into becoming short term members of his group.
Nightwing: Other then Batman, Nightwing was the first hero to join Batman's side as his sidekick, Robin. He eventually became his own hero but remains a close ally of Batman's.
Robin: Tim Drake also known as Robin III was the latest to join Batman's crusade as his newest sidekick and currently the closest ally to Batman.
Oracle: Similar to Nightwing, Batgirl was one of the first to join the Batfamily, although she wasn't accepted until Dick's arrival she was always an ally of Batman. After becoming Oracle, she remains as a close ally to all of the Batfamily.
Red Hood: Formerly Robin II, Jason Todd was a close ally of Batman's until his untimley death. After his revival Jason became an anti-hero to Batman, going against what Bruce had taught him as a hero. Even so Jason remains loyal to Batman from a distance, still admiring his adoptive father.
Catwoman: A former big time criminal and master theif, Catwoman was once one of BAtman's greatest enemies. Yet the two seemed to have a special connection, Catwoman was semi-reformed into becoming Batman's ally while remaining as an anti hero/