The current members of the Bat Family are in order of appearance:

Batman
Nightwing
Robin
Oracle
Azrael
Batgirl

At the moment Huntress cannot be considered to be an official member of the Family.

Batman: Gotham Knights is the new Batman ongoing title that replaced Shadow of the Bat from January 2000 onwards. Knights seems to have been designed to act as a Batman Family title. The seventies Batman Family series was an anthology featuring stories about the different members of the family, it didn't tell team up stories between the various members of the family. The name Gotham Knights had actually been around for some years before the new title started: in Batman: The Animated Series it was the name of a football team; prior to that it was the name of a baseball teamin the American League, Eastern Division (according to the Atlas of the DC Universe, 1990, which is a role-playing sourcebook so the name may not have been used much, if at all, in the comics).

Vic Sage: "...It comes back to you and the Batman. Don't you see it? He created you by setting an example. And as with all parents you struggle against him, seeking both approval and liberation."
Helena Bertinelli: "You saying that Batman is my father?"
VS: "In a manner of speaking...Yes."
HB: "You are so full of it." Batman/Huntress: Cry for Blood #4

Knights, on the other hand, isn't an anthology it's a normal 22 page lead story with an 8 page black and white backup. The lead stories will feature stories that involve Bats and other members of the family, although not every issue will feature other heroes.

Batman: "You don't think family's important to him[James Gordon]? Especially now after losing his wife? What makes you think he'd be more concerned with them [Babs real parents] than with you?"
Barbara Gordon: "What makes me think that? YOU! You make me think that!"
BG: "You who raised somebody else's kid, too, except that as wildly devoted as he's been to you all this time you've been so preoccupied with your dead parents that you've barely acknowledged he's there! You have this whole family that isn't real to you because they're not blood!" Batman: Gotham Knights #6

Prior to No Man's Land Detective Comics was the title in which these type of stories were most likely to be found, particularly stories about Batman and Robin. Gotham Knights #5 involved Batman, Robin, Azrael and Batgirl, Gotham Knights #6 tells a great story about Barbara Gordon and her relationship with Batman and James Gordon, #7 featured Alfred and Dr. Leslie Thompkins. By using a narrator the early issues of Gotham Knights can be seen as a primer on the histories and relationships between the members of the Batman family.

No Man's Land also saw the introduction of a new Batgirl.

There are now other characters that also have their own titles who aren't part of the family, Catwoman was the first Batman supporting character to receive their own series in the nineties expansion, although both The Joker and The Huntress had previously had their own ongoing series. Another Batman character has been given an ongoing series that will be starting soon, Harley Quinn. Everyone's favourite character from the animated series was introduced into the DCU proper during No Man's Land. Neither of them are members of the family because they are both villains. Birds of Prey is also produced through the Batman editorial offices but Black Canary isn't part of the family; Canary has appeared in various Bat titles from time to time but has probably too much history with other characters in the DCU. Black Canary was a founding member of the Justice League in current continuity and is a member of the new Justice Society.

Lest it be forgotten, there are other characters who play crucial supporting roles in the Batman Family, Alfred Pennyworth and Leslie Thompkins. Catwoman has also worked with various members of the Bat Family, mainly because whenever there is a major crossover in the Bat titles every ongoing series ends up being involved at some point: see Knightsend, Contagion, Legacy, Cataclysm and No Man's Land.