Disclaimer: Most of this information is directly from the site Salvation. I found a lot of interesting information here that I had never noticed in the series.
The first slayer was introduced in the season four finale "Restless". Little is known about this mysterious slayer but a meeting with this predecessor creates a longing to know the origins of her duty in Buffy. Her main role is telling Buffy that "Death is your gift." This is a foreshadowing of when Buffy must end her life to save her sister Dawn and the world. This slayer also tries to kill off all of Buffy's friends through their dreams. She did this in order to make Buffy fight alone like all other slayers had done in the past.
In 1845, Boston shipyards were plagued by a series of grisly murders. The attacks ended when a quiet young woman arrived in town.
In 1866, the disappearance of Civil War widows shocked an already grieving community. These disturbing events came to an end when Lucy Hanover set up camp in a nearby graveyard.
In 1893, in the Oklahoma Territory, a series of savage attacks claimed the lives of 17 homesteaders. The murders stopped when a young woman blacksmith passed through town.
1897, in Wyoming, a string of bizarre murders shocked a small, inside community. The killings ceased shortly after twenty year old Florence Gilbert arrived in town.
Twenty two New Yorkers lost their lives in the 1912 boarding house murders. The killings ended abruptly when a stubborn nurse named Arabelle Gish sought lodgings in room number six.
Chicago, 1927. Over a period of two weeks, forty-one bodies were found near Union Station. Shortly after the arrival of the young woman to the right, the murders stop.
Seen for the only time in "Fool for Love", this Chinese slayer was called during the time of the Boxer Rebellion. After facing Spike in an impressive sword fight, she is drained and killed by him.
Also seen for the only time in "Fool for Love" is this New York City slayer who was called in the 1970's. Nikki fights with a free style similar to Buffy, but loses her final battle to Spike, who snaps her neck in a subway train.
Called in 1993 and died in 1996, India was the slayer whose death activated Buffy. Featured in the Nancy Holder book, "The Book of Fours", India is trapped in the ghost paths and must be saved by Buffy, Kendra and Faith.
Buffy Summers is the current slayer and our heroine. She protects Sunnydale from the Hellmouth with the aid of her friends and her watcher, Giles. She once died facing The Master, but was revived, and again by closing a portal with her blood to save her sister's life. Buffy is different from the other slayers because she has the ability and resources that the others did not. For example, she has Xander, Willow (a Wiccan witch), Anya (a vengance demon), and Giles (her watcher), to guide and help her. She is also different because she is more rebellous. She dates vampires (Angel and Spike) and she continues to have an open, outgoing life (which is forbidden by the watchers convention). Finally, Buffy is the only slayer that had the ability to come back from the dead numerous times to re-save the world.
Kendra was the Jamaican slayer called to replace Buffy after her death. They were both shocked to find that there are now two slayers. Kendra has a different watcher who is much more strict than Buffy's. She is all about following traditions of the slayer and she is shocked by the way that Buffy lives and acts. Kendra was killed by Drusillia in "Becoming Part One" and Buffy is framed for the murder.
Called to replace Kendra, Faith becomes evil after the killing of a human. She joins forces with Mayor Wilkins and helps him in his plots. After the mayor's defeat, she moves to LA where Angel helps her with a change of heart. Faith killed her first watchers and she believes that she does not need guidence from anyone. Buffy and Faith fight a lot and become known enemies. In one episode, Faith is able to cast a spell and take over the body of Buffy and put Buffy in her body. This is important because the watchers council is out to get her when she becomes evil. Overall, I believe that Faith was the most modern slayer in a rebellious sense.
Melaka Fray is a slayer from far in the future, a teenage girl from the rough side of town who is about to find out that she's the chosen one. Introduced in the Dark Horse comic series, written by Buffy creator Joss Wheldon.
Sources
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Most of this information is from an excellant site titled Salvation:
http://www.buffysearch.com/
http://callie.csci.unt.edu/~ghartwig/sounds/buffy.html