'Oh, he knows how to play, little bitty baby Potter. Very well, then -'
--Bellatrix Lestrange (OP35)
"Never used an Unforgivable Curse before, have you, boy? You need to mean them Potter! You need to really want to cause pain -- to enjoy it -- righteous anger won't hurt me for long -- I'll show you how it is done, shall I? I'll give you a lesson."
-- Bellatrix Lestrange (OP36)
Bellatrix Lestrange was one of Voldemort’s most devoted Death Eaters, a cruel and vicious woman who was guilty of torturing and murdering wizards and Muggles alike. Bella, as she was sometimes called, was the oldest daughter of Druella Rosier and Cygnus Black of the “Noble and Most Ancient House of Black.” Her sisters are Narcissa Malfoy and Andromeda Tonks. A particularly enthusiastic member of Voldemort’s inner circle of Death Eaters, Bella relishes causing pain, especially when her victims are powerless; her specialty is the Unforgivable Cruciatus Curse.
She is also capable of tremendous loyalty. During Voldemort’s first reign of terror, Bella and Lucius Malfoy were so high in Voldemort’s trust that they were each entrusted with one of his Horcruxes. Bella was given the Hufflepuff cup which she secured in the Lestrange family vault deep in Gringotts.
Having successfully avoided capture and imprisonment in the immediate aftermath of Voldemort’s fall, she (together with three other Death Eaters) attempted to find and restore Voldemort, torturing Frank and Alice Longbottom into madness for information. For this she was given a life sentence in Azkaban prison (GF27, GF33), where she was held until her escape more than 14 years later. After her escape, Bella took part in the Battle of the Department of Mysteries, where she managed to defeat her cousin Sirius, sending him falling through the ancient veiled archway in the Death Chamber (OP35).
Bellatrix’s snarling conversations with fellow Death Eater Severus Snape in Spinner’s End (HBP2) was designed to discover his loyalties, but in the end it was his willingness to perform the Unbreakable Vow with Narcissa, agreeing that he would protect Draco and kill Albus Dumbledore if Draco failed, that convinced her that Snape could be trusted.
After Dumbledore’s death, Snape was ascendant in Voldemort’s trust, and the Malfoys and Bella were singled out for humiliation; Bella was taunted and told to “prune” the Muggle-born and half-blood members of her family tree. So when Greyback and the snatchers captured Harry, Ron and Hermione with the Sword of Gryffindor, she panicked. The sword should have been in her vault at Gringotts, so she assumed it had been breached and delayed telling Voldemort that Harry had been captured. She couldn’t bear falling further from favor because the cup might have been stolen from its hiding place along with the sword. Unfortunately for Bella, she dithered too long. Dobby appeared and helped Harry, Ron and Hermione (and others) escape the mansion, knowing exactly where to find one of the last Horcruxes. To Harry’s deep sorrow, Bella killed Dobby with an accurately-thrown knife. Bella survived Voldemort’s fury and later fought in the Battle of Hogwarts where she was killed by Molly Weasley.
Bella had the aristocratic Black good looks: tall with black hair and (in her case) heavily-lidded eyes and air of arrogance; although as with Sirius, Azkaban left its mark (GF30, OP25).
Born: 1951 (day and month unknown) (BFT).
Died: May 2, 1998, killed by Molly Weasley (DH36, YL).
Hogwarts: Slytherin (GF27, OP6, OP23, OP25, OP33).
Since Bella was born in 1951, she started Hogwarts in 1962 or possibly 1963 if she was born after September 1.
Father: Cygnus Black (1929-1979) (BFT).
Mother: Druella Rosier (BFT).
Sisters: Narcissa (Black) Malfoy and Andromeda (Black) Tonks.
Husband: Rodolphus Lestrange (OP6), though Voldemort was her only love (BLC).
Cousins: Sirius and Regulus Black.
Nephew: Draco Malfoy.
Niece: Nymphadora Tonks.
Appearance
Eyes: Dark, heavy-lidded.
Hair: Long, black hair (DH26) .
Other characteristics: Tall, with a harsh voice, and a thin mouth.
Pre-Azkaban: had thick, shining hair (GF).
Post-Azkaban: face is gaunt and skull-like (GF).
Wand: Walnut and dragon heartstring, 12 & 3/4 inches, unyeilding (DH24). Captured by Harry during their escape from the Malfoy mansion and given to Hermione for her impersonation of Bella at Gringotts.
Known murders:
Family
Ancestry: mostly pure-blood; descendants of mixed blood are not recognized by the family. 
Family in general: "The Noble and Most Ancient House of Black" (OP6); Sirius' parents were convinced that to be a 'Black' made you "practically royal."
Family crest is mentioned in OP6 but not described; however, Rowling drew it on her Black Family Tree. It shows a shield with greyhounds rampant charged with a chevron, 2 five-pointed stars and a short sword. In the formal language of heraldry, it is: "Sable, a chevron between two mullets in chief and a sword in base, argent." (Thanks to Richard for the terminology).
Family motto: Toujours pur ("always pure" in French) (from tapestry in OP6 and BFT).
Tapestry: a tapestry exists at number twelve Grimmauld Place that has, according to Kreacher, been in the family for seven centuries (OP6). On it the family's births, marriages and deaths are embroidered with gold thread; family members who have been disowned have been "blasted" from the fabric (a small burn like a cigarette burn is where their name is).
Important sources of information on the Black family: OP4 where we meet the portrait of Sirius' mother; OP6 where Sirius explains the Black family tapestry to Harry, and the Black Family Tree, a hand-drawn tree that Rowling donated to Book Aid International in January of 2006. We believe that this tree is meant to represent a portion of the tapestry.
Skills
Bellatrix was a Legilimens who gave nephew Draco Malfoy Occlumency lessons, Duelling, Cruciatus Curse, Killing Curse, knife-throwing
Other canon notes and references
In spite of her marriage to Rodolphus Lestrange, Bellatrix had a secret child with Lord Voldemort. She gave birth at Malfoy Manor just before the Battle of Hogwarts, and after her death, the child named Delphi was given over to be raised by "extreme Death Eater" Euphemia Rowle, who kept a mournful bird known as an Augurey in a cage. Delphi took the Augurey as her symbol, having it tattooed on her back, and vowed to someday resurrect her father, The Dark Lord (CC3.16, CC3.19, CC4.11)
Commentary
Etymology
'Bellatrix' is Latin for "female warrior;" also the name of a brilliant star in the constellation Orion that is sometimes called "the Amazon star."
'Lestrange' could refer to Roger L'Estrange, a 17th-century English journalist who was very much against religious tolerance (Cambridge History of English and American Literature).
Notes
After the Potters died and the Dark Lord was vanquished by baby Harry, Bellatrix and her fellow Death Eaters tortured Frank and Alice Longbottom into insanity. Bellatrix didn't know anything about the prophecy, and targeted the Longbottoms because they were Aurors who might know if Voldemort was alive or dead. This was confirmed by the author in the "Rumours" section of her Official Site:
The Lestranges were sent after Neville to kill him
No, they weren’t, they were very definitely sent after Neville’s parents. I can’t say too much about this because it touches too closely on the prophecy and how many people knew about it, but the Lestranges were not in on the secret. (JKR)
Although Bellatrix was married to Rodolphus Lestrange, her heart belonged to Lord Voldemort alone, according to the author:
And Bellatrix, was, as I think is clear-- you know, I doubt that people will be particularly shocked to hear, 'cause I'm sure they've deduced, that Bellatrix is madly, romantically in love with Voldemort. This is-- you know, that's the obsession of her life (PC/JKR2).
Question: Did Bellatrix ever love her husband, or did she have love only for Voldemort
J.K. Rowling: She took a pureblood husband, because that was what was expected of her, but her true love was always Voldemort.
It is particularly ironic that the love of her life was a half-blood with a Muggle father, since she was also obsessed with blood purity. Of course what especially drew her to Voldemort was his quest for power and love of torturing people. Her pureblood husband, while he showed up at the Battle of the Department of Mysteries, never says one word in the books - a complete non-entity compared to Voldemort.
This obsession with the Dark Lord was also the reason Rowling wanted Molly Weasley to kill Bellatrix instead of Neville Longbottom, who had an even greater reason to get revenge due to his crippled parents.
I wanted it to be Molly, and I wanted it to be Molly for two reasons.
The first reason was I always saw Molly as a very good witch but someone whose light is necessarily hidden under a bushel, because she is in the kitchen a lot and she has had to raise, among others, Fred and George which is like, enough… I wanted Molly to have her moment and to show that because a woman had dedicated herself to her family does not mean that she doesn’t have a lot of other talents.
Second reason: It was the meeting of two kinds of – if you call what Bellatrix feels for Voldemort love, I guess we’ll call it love, she has a kind of obsession with him, it’s a very sick obsession … and I wanted to match that kind of obsession with maternal love… the power that you give someone by loving them. So Molly was really an amazing exemplar of maternal love. … There was something very satisfying about putting those two women together. (OBT/CH)
Bellatrix in the Movies
The role of Bellatrix in "Harry Potter and the Order of the Phoenix" was initially given to Helen McCrory (IMDb), but when she became pregnant the role was recast and given to Helena Bonham Carter (IMDb).
From the Web
Bellatrix Lestrange: Sadist, or No? by lenore_telltale
Harry Potter and the Order of Archetypes: Bellatrix Lestrange, the Disciple by Katie Majka
Pensieve (Comments)
Tags: Bellatrix Remembrall children cruel dark love Narcissa Remembrall obsession sadistic torture