Muggles' Guide to Harry Potter/Characters/Bane

Overview
Bane is a Centaur living in the Forbidden Forest.

Philosopher's Stone
When Harry is serving his detention in the Forbidden Forest with Hagrid, they are startled by the appearance of a centaur, Ronan, who makes some comments about astronomy ("Mars is bright tonight"). Shortly, Bane joins them, and makes similar comments about astronomy.

After leaving them, Harry, Draco Malfoy, and Hagrid's boar-hound Fang find the creature that has been killing Unicorns. As the creature seems to be about ready to attack Harry, he is rescued by another Centaur, Firenze, who offers to carry Harry back to Hagrid. As he is doing so, he is met by Bane and Ronan, who accuse him of becoming a pack animal for humans, like a donkey, and interfering with the portents. Firenze leaves them behind, saying that he will fight the evil, even alongside humans if he must.

Order of the Phoenix
Firenze, now teaching Divination, explains that he cannot return to the Forbidden Forest, as he has been banished by his herd. Harry sees a hoof-shaped bruise on his chest, and wonders if it was Bane who put that there.

Bane, along with Magorian, is in the group of centaurs who confront Hagrid as he is taking Harry and Hermione back to the school after introducing them to his half-brother, Grawp. Bane makes no sign of having spoken to Harry earlier, but warns "this human" Hagrid what will happen to him if he returns to the Forest.

Bane is among the group of centaurs who come to investigate when Hermione is leading Harry and Dolores Umbridge into the Forbidden Forest to try and entrap her there. After Umbridge has insulted the Centaurs by calling them "inferior half-breeds" and has magically bound Magorian, the centaurs swarm her, and the last we see of Umbridge is Bane bearing her off into the forest.

Deathly Hallows
When Hagrid is carrying an apparently-dead Harry out of the Forbidden Forest, apparently several centaurs are present and watching Lord Voldemort's victory procession. Hagrid calls out to Bane, apparently believing that their inaction implicates them in Harry's death.

Whether or not Hagrid's accusations of Bane have effect is uncertain; Bane, however, is one of the centaurs who lead the counter attack on the Death Eaters, along with Ronan and Magorian.

Strengths
Astronomy and reading the stars and planets.

Relationships with Other Characters
Bane is part of a herd of centaurs that includes Ronan, Firenze and Magorian. While the herd seems to choose to separate itself from human affairs, Bane is something of an extremist in these views. We have little information on how his extremism affects his relations with many of the other centaurs in his herd, though we suspect that he and Firenze had a falling-out when Firenze elected to accept the Astrology post at Hogwarts.

Analysis
In his own way, Bane is as prejudiced as any Death Eater. He believes in the innate superiority of Centaurs over humans, and is affronted by any suggestion that humans and centaurs could work together. In this he is only echoing the beliefs of his herd, beliefs that are apparently shared to a greater or lesser degree by every centaur we meet.