1st Division Captain - Yamamoto Genryuusai Shigekuni

First Division Captain and founder of the shinigami academy. By virtue of his position and seniority, he is also the supreme commander of the Gotei 13.
Yamamoto-taicho looks like a very old man, almost after the fashion of the Taoist Immortals, but under his shinigami robes he still has a strong body that has not decayed with age. His spiritual pressure is possibly greater than any other being in Soul Society; it was enough to paralyze Ise Nanao--the Eighth Division Vice-Captain--with a mere glance. He wields Ryuujin Jakka, the strongest of all fire-type zanpaku-to. His skill in kidou is unknown, but probably as formidable as his swordsmanship, as he appears to embody the convention of the "old master."
Kyouraku Shunsui (8th Division Captain) and Ukitake Juushiro (13th Division Captain) seem to have a particularly strong relationship with Yamamoto-taicho. He mentions that they were the first graduates of his shinigami academy to rise to the rank of Captain, and some clips from the anime show Yamamoto-taicho sparring with the two (and easily winning).

2nd Division Captain - Soi Fong

Captain of the Second Division, and Commander of Covert Operations and Executive Militia.
Not much is known about Soi Fong. She is from a lower noble that served the great Shihounin family, and became a comrade of Shihouin Yoruichi (former Captain of the Second Division) at a young age.
In combat, Soi Fong wields Suzumebachi, one of the more unique Zanpaku-to. She also seems to have the entire Covert Operations division at her beck and call, ready to fight at a moment's notice.

3rd Division Captain - Ichimaru Gin

The sly-faced, perpetually smiling Ichimaru seems to be almost totally amoral, willing to injure even his own comrades if it helps him get what he wants.
Ichimaru's personality is inscrutable. It is impossible to tell if his ever-present grin is merely a facade to hide his true thoughts, or if he really does take devilish glee in the various tragedies he sets in motion.
As with most captains, Ichimaru's past is shrouded in mystery. However, he seems to have a rather strong relationship with vice-captain Matsumoto, who is probably his only true friend.
Ichimaru's zanpaku-to is Shinsou, which he uses with impressive skill, if rather indiscriminately.

4th Division Captain - Unohana Retsu

A kind and peaceful woman, who is perfectly suited to be Captain of the healing-oriented Fourth Division. She seems willing to help almost anyone in need, but don't let her motherly appearance fool you; she is highly intelligent and possesses an extremely strong will.
Though possessed of a compassionate personality, Unohana ultimately remains loyal to the core principles of the Gotei 13 and Yamamoto Genryuusai, even at times when she seemingly feels that official policy is not the right course of action.
She has not engaged in any combat to date, but wields the healing zanpaku-to Minazuki as her blade of choice.

5th Division Captain - Aizen Sousuke

A rather unassuming individual, but one with great depth. Sousuke is a brilliant thinker and fighter--probably the second most powerful captain after Yamamoto--and is respected among shinigami for his chivalrous demeanour. He seems to be wary of Ichimaru Gin and his motives.
He acts gently toward his subordinates, particularly Hinamori Momo, his vice-captain. He recognizes the respect she has for him, and plays along with her hero-worshipping.
His zanpaku-to is the amazingly devious and powerful Kyouka Suigetsu.

6th Division Captain - Kuchiki Byakuya

Captain of the Sixth Division. Byakuya is head of the noble Kuchiki family, and as such is sophisticated in his philosophy and manner of speech. He is perpetually cool and collected--many might say cold and emotionless--having never been seen to either smile or lose his temper.
Despite his youthful appearance, Byakuya is actually a widower. His wife died some years ago, seemingly of one or another illness. It is not known whether Byakuya's reserved personality developed or increased after his wife's death, but it seems a logical assumption.
He is Kuchiki Rukia's adoptive brother, but does not appear to possess or display much filial affection. Rukia even goes so far as to say at one point that Byakuya never once cared for her in the slightest. This may be a somewhat unfair portrayal, however, as Byakuya seems to be the type who keeps his cards close to his chest, so to speak.
His weapon is the deadly Senbon Zakura, which he wields with suitable elegance to dispatch his foes.

7th Division Captain - Komamura Sajin

The huge Captain of the Seventh Division. Komamura is a mysterious individual, hiding his features from view with a large helmet. He has a great sense of honour, being particularly devoted to Yamamoto Genryuusai. He is close friends with Tousen Kanamae of the Ninth Division. They share similar life philosophies, though Komamura is seemingly less gentle or hesistant in his approach than Tousen.
When it comes time to fight, Komamura wields the niftily named Tengen, a blade with size to match his own.

8th Division Captain - Kyouraku Shunsui

The creatively dressed Eighth Division Captain. As his overcoat, hat, and stubble might indicate, Shunsui is someone who lives life in a carefree manner. He loves to nap, joke, drink, and generally be laid-back about everything that comes his way. When things get serious, however, Shunsui shows that beneath his whimsical exterior lies intelligence, skill, and a sensitive and compassionate character that hates to watch suffering.
Shunsui has an excellent relationship with his vice-captain (if somewhat love-hate on her part), and is also good friends with Thirteenth Division Captain Ukitake Juushiro, who, along with Shunsui himself, was one of the first graduates of Yamamoto Genryuusai's shinigami academy. It seems that Shunsui also has a good relation with Yamamoto, having coined the nickname "Yama-jii."
When Shunsui is forced to fight, he wields the twin-blade zanpaku-to Katen Kyoukotsu with awesome skill.

9th Division Captain - Tousen Kaname

The blind Captain of the Ninth Division. Despite his disability, Tousen is a capable fighter with a strong sense of justice. He is also a staunch advocate of taking the path that leads to the least amount of violence. This outlook is shared by his good friend Komamura Saijin. Tousen is, therefore, highly suspicious of Zaraki Kenpachi and the battle-loving Eleventh Division, which he believes may one day plunge Soul Society into bloody chaos.
When the situation demands it, he wields the powerful Suzumushi with skill that belies his blindness.

10th Division Captain - Hitsugaya Toushiro

The Tenth Division Captain is the youngest captain in the Gotei 13 by a considerable margin. He is known as a prodigy in study of the shinigami arts, earning him the nickname of "Tensai," or "Genius."
Despite his youth, Hitsugaya is one of the more mature captains, level-headed and perceptive, if a bit lacking in the humour department. Unlike the unemotional Kuchiki Byakuya, however, the right set of circumstances will put Hitsugaya into anger, annoyance, etc.
Hitsugaya seems to get along well with just about everyone except Ichimaru Gin, whom he mistrusts. He has a particularly strong relationship with Hinamori Momo, and also has a strong bond with his vice-captain, Matsumoto Rangiku.
When battle comes around, Hitsugaya wields Hyourinmaru, the most powerful ice-type zanpaku-to in Soul Society.

11th Division Captain - Zaraki Kenpachi

The bloodthirsty Eleventh Division Captain. Zaraki lives for one purpose and one purpose only: to fight. All other concerns are basically secondary. Though Zaraki enjoys fighting with all his strength, he does not seem particularly concerned with winning or losing; the joy of battle is all that matters to him.
Zaraki was originally a nameless swordsman fighting for his life on an apparently daily basis. After much trial, he was spotted by the shinigami and given a position in the Gotei 13, where he rose in the ranks until finally defeating (and, incidentally, killing) the previous Eleventh Division Captain in single combat.
That's not to say that Zaraki doesn't have a softer side, though. He has an unlikely friendship in Kusajishi Yachiru, whose tiny, cute appearance and saccharine personality stand in stark contrast with Zaraki's massive physique and gruff manner. The two are inseperable, however, like father and daughter, and it's safe to say that Yachiru is the only person whom Zaraki's wrath has no chance of touching.
Wielder of a nameless blade, Zaraki is the only captain in Soul Society who does not know the name of his zanpaku-to; this is a testament to his terrifying strength in combat and colossal spiritual pressure.

12th Division Captain - Kurotsuchi Mayuri

The epitome of a mad scientist, and hence perfect for the job of Twelfth Division Captain. Mayuri paints himself black and white, wears a strange hat, and has altered his body to grant it many strange abilities. His main goal appears to be pursuit of forbidden knowledge at any cost, and he does not hesitate to resort to sadistic or underhanded methods to achieve his ends. Life means nothing to him; he would turn his own men into living bombs if it meant he could do or learn something more easily.
Though Mayuri is completely cold and cruel to everyone he meets, he does have one loyal supporter in the form of his "daughter," Nemu. She is completely devoted to her master, uncomplainingly taking all manner of abuse and even wishing against his death.
On the frequent occasions when Mayuri wants to fight or perhaps revel in a bit of sadism, he wields the bizarre but lethal Ashisogi Jizou.

13th Division Captain - Ukitake Juushiro

The Captain of the Thirteenth Division, with an almost legendary reputation for being a nice guy. Sadly, Ukitake has frail health and is ill a lot of the time, but in his better moments he is a strong and reliable fighter as well as a caring and compassionate leader.
His best friend seems to be Shunsui, with whom he was a fellow student in the early days of Yamamoto Genryuusai's shinigami academy. However, the entire Thirteenth Division seems to love and respect their captain with almost fanatical fervour, and he may thus be said to be a friend of all his subordinates, though not notably close to any of them. Of course, as Kuchiki Rukia's former captain, he is quite concerned as to her eventual fate.
On the rare occasions when he is both in good health and inclined to fight, Ukitake wields Sougyo no Kotowari, one of only two twin-bladed zanpaku-to in all Soul Society.