Chado Yasutora

Chado Yasutora is actually a Mexican guy who kinda grew up in Japan where he met Ichigo. Back at Mexico he was known to pick fights like a normal day routine which is completely opposite of how he is being portrayed as someone who wouldn't fight - which Ichigo finds it wierd. Chado helped Ichigo once when he got picked by a group of goons who were pissed off with his orange hair (or something like that) and beated the hell out of Chado instead, and this is where their friendship began. This is when Chado first heard the term "I'll hit for your sake and you'll hit for my sake" which he later told one of the Captains when they were trying to save Rukia from being executed later during the series.

Chad also seems to have some minor/unrefined abilities to sense hollows. He also seems to be a pacifist.

Kuchiki Ruchia

I would like to state that Ruchia gave up her powers. The fact that she could not get them back was an unforseen consequence. Let's not forget that Ichigo reminds her strongly of her former luitenant, one of the most important people in her life right until his death. She is a lost soul who puts up a brave face while waiting for her powers to return, resourceful and quick. When she returns to soul society the extreme circumstance does not really allow you to get to know her better. She has this annoying way of explyning herself using drawings which leaves others more confused than before.

Ishida Uryu

Ishida Uryuu is introduced into the Bleach universe as the last remaining Quincy (Destroyers) - a race of humans who made it their goal to eliminate all Hollows (which they justified as an act of revenge, for all the acts the Hollows had committed, and for all the lives of their brethren they had claimed). They were always at odds against their rivals, The Shinigami (Death Gods), who do not destroy Hollows, but perform "Soul Burials" on them instead - either sending them to Soul Society or Hell, depending on the actions they took in their lifetime.
The Shinigami opposed the Quincies, as the destruction of so many Hollows unbalanced the natural cycle between the realms, which would ultimately lead to the end of the world. Both sides would not heed the others' views and thus lead to a bitter conflict between the two.
This eventually resulted in the extermination of the Quincies by the Shinigami some 200 years before the current timeline in Bleach.

When Ishida Uryuu makes his first appearance, he sets himself up as Ichigo's rival, claiming he hates all Shinigamis, and subsequently challenges Ichigo to a competition between the two of them, in an attempt to prove that the Quincies are stronger, and The Shinigamis unnecessary. He unleashes an "Anti-Hollow bait" that attracts many Hollows to Earth's realm.
Both manage to handle themselves well to begin with, but it is revealed as time passes that alot more are appearing than he expected, and both him and Ichigo struggle to keep up with the constantly replenishing hordes they each encounter.
When the two rivals encounter one another again (during the same battle), it is revealed that the real reason why Ishida hates Shinigami is because he saw his grandfather (who was also his sensei, and a Quincy) die in front of him, when he was young. The old man could relate to the Shinigamis' views about the Quincies, and why they had to do what they did. He also wanted to team up with them, combining the strength of the two sides into a single powerful coalition in the fight against the Hollows. The Shinigami flatly refused, and on the day of his death, they arrived too late to save him from some Hollows. Ichigo corrects Ishida however, in that his sensei did not want such a wish as this to be realised as means to prove the strength of the Quincy to the Shinigami, but instead genuinely desired for the two sides to work together in unison.
They decide to team up in a final stand, as this is their only hope of survival. They hold their ground, until Ishida sees an extremely large Hollow ("Menos Grande") coming through the crack in the sky. Just then, Urahara and co. come to take care of the small fry, while Ichigo and Ishida are given the chance to take on the Menos Grande. Their attacks seem to have no effect on the giant Hollow, and when, in an attempt to get Ichigo's attention, Ishida grabs Ichigo's zanpakutou ("Soul Slayer"), Ichigo's large spiritual power flows through Ishida and his spirit-bow grows enormously. He asks Ichigo to control it, realising that the combined strength of the two could defeat the Menos Grande if they could somehow utilise it. Ichigo says he has no idea what he is talking about (and does not know how to control his soul's level of power), and that perhaps his power is always at its fullest. Nonetheless - with Ichigo's zanpakutou tied to his head - Ishida prepares to attempt to fire a large spirit-arrow at the Hollow, but Ichigo stops him (saying it's a stupid idea) and charges at the Menos Grande alone, instead. The Menos has been charging up a large ball of energy, and now fires this at Ichigo, and as he is struggling to block this, Ishida - sensing the power of Ichigos' riatsu (spiritual pressure) - realises that he can't be using it at full power all the time, as it would eventually run out. Just then, Ichigo deflects the energy ball and slashes at the Menos, wounding it and causing it to retreat back into the realm of the Hollows. Ichigo subsequently collapses, as due to the fact that he released all of his spiritual energy at once, he is now overflowing on his own power, and will die if he cannot not release it. As Ichigo cannot control it, Ishida has to act as his outlet for releasing it, and consequently saves Ichigo by continually firing off spirit-arrows while Ichigo's excessive power is pouring through him from his zanpakutou. Despite the fact that Ishida is receiving bleeding wounds from this act, he continues until Ichigo is safe.

From these sequence of events, they both earn respect for one another and become allies.

Ishida volunteers to travel with Ichigo (and the others) to Soul Society to help save Kuchikia Rukia from execution during the "Soul Society arc". He trains extremely hard in preparation, donning his grandfather's glove, which is an extremely powerful tool that only the strongest of Quincies can withstand using - nevermind perfect - which he practises with, rigorously for days on end, eventually mastering it's grand potential.

When they first enter the Shinigami's grounds ("Seireitei"), Ishida is paired off with Inoue Orihime, and they spend a large chunk of that arc together. Ishida clearly cares for Inoue, and is very protective of her, both physically, and also in the sense that he is always conscious of her emotional state as well. He saves her life on more than one occasion, and has also protected her from other types of "danger" (if you see what I mean). They have great chemistry, and Inoue also cares a great deal for, and admires Ishida (and also saves him a few times herself), but she is seemingly unaware of the true extent of his feelings for her. Whether she will ever catch on, and reciprocate such feelings with him remains to be seen, especially since she is so obsessed with Ichigo at the moment.

During this arc, Ishida also has a dark, and emotional encounter with one of the Gotei 13 - the 12th Division captain, and head of the experimental science department, Kurotsuchi Mayuri, who is revealed to have been the cause for the delay in the arrival of the Shinigami when Ishida's grandfather/sensei died at the hands of Hollows. Mayuri further reveals that this was intentional, as he wished to study and experiment on a Quincy, and even goes as far as to show Ishida a photo of his grandfather after he had finished with him. A dramatic battle between the two ensues, with Mayuri eventually having to release his "Bankai" (second zanpakutou form) against Ishida, and with Ishida likewise releasing his most powerful form too. He breaks the seal on his grandfather's glove, producing a vastly superior bow, with extreme power, which draws in large quantities of spiritual energy from his surroundings (this is how Quincies use their power generally, also). It also increases his own riatsu's power, enabling him to move at much higher speeds.
He proceeds to beat Mayuri, causing him to resort into turning into a kind of goo (which he had developed as a last ditch survival technique) and escape indignantly down the cracks of the walkway where they fought, as his body was too badly damaged, and required a long period of healing for it to ever truly recover. Though he had defeated Mayuri in combat, he had become poisoned through his bankai, and would have surely died if not for the 12 Division Vice-captain's aid. Supposedly, in return for "letting" Mayuri survive, Kurotsuchi Nemu (who is a loyal slave to Mayuri, formed of his own DNA) gives Ishida the antidote required to cure him of the poison.
During the battle, under the command of Mayuri, she sacrifices her own safety by grabbing Ishida while Mayuri stabs through her and into Ishida. However, her role in this attack wasn't fully realised, as she seemingly hesitated, as although she is loyal to, and created from Mayuri, she is naturally a kind and gentle person (which is probably a side effect of making her so submissive and subserviant). As a consequence, Mayuri beats on her in his disappointment.
Ishida's caring side comes through here again, as he shouts for Mayuri to stop several times. At this point, he is also temporarily and partially paralysed due to Mayuri's attack - his zanpakutou's ability is that it causes whichever limb it hit to stop responding to the brain's commands. Ishida later uses a technique to control that limb through spiritual power though anyway, making its ability obsolete in his case.
Anyway, as it is, Nemu's true motives could be considered questionable, as due to her actions for Ishida later again (curing him of Mayuri's poison) it could be suggested that she in fact cares for Ishida (specifically) somewhat too. They both share at least some form of chemistry when she is aiding Ishida's recovery, as they are both more concerned with each other's injuries than their own.
Ishida even offers for her to drink from the anidote first, but she refuses, saying she does not require any of it (she is immune to the poison, as she shares Mayuri's DNA), and that he should have it all to himself. He obliges, as this makes sense anyway, but he still remains concerned for her injuries, but she passes them off as nothing for him to worry about.
Their inherent trust of one another also suggests some chemistry.
Maybe this will be developed further into the story, who knows.

Thus, consequently, Ishida survives the battle, but at great cost - when a Quincy breaks the seal on the glove, and after releasing the power it gives them, he or she will lose all of their Quincy powers.
Nonetheless, he continues his mission to save Rukia and heads towards "The Towers Of Penitence", but is stopped in his tracks by 9th Division's Captain, Tousen Kaname, who knocks him unconscious with his zanpakutou's supersonic ability. He awakes later to find himself imprisoned (along with fellow comrades Chad Yasutora and Shiba Ganju) but is soon broken out of prison by none other than the 11th Division Captain, Zaraki Kenpachi, who wants their aid in finding Ichigo (just to fight with him again, of course!)
After this, he acts pretty much as just an observer for what little remains of the rest of this arc.

Later in the manga, it is also revealed that Ishida's father is a Quincy as well, and he offers to help Ishida regain his Quincy powers, but only if he agrees to never associate with the Shingami again (this is because his father was in opposition with Ishida's grandfather, in that he still holds a grudge against the Shinigami, and disagrees with their ways).
Ishida agrees outright.