Onizuka used to be Yankee, a Japanese delinquent. His best friend is Danma Ryuji and with him he's part of the Onibaku Duo (Oni for Onizuka and Baku for Bakudan which means Bomb.) Back in his younger days, Onizuka used to have a lot of street fights with people trying to be better than him. As the Onibaku was reputed unbeatable, his opponents were not above Kick the Dog and Moral Event Horizon on him and his friends. Bad luck for them, Onizuka used to get a little Ax-Crazy when pushed too much. He then left Shonan, faking his death in front of his friends. He then moved to Tokyo. Since then, Onizuka became a teacher and softened up a bit.
Catchphrase: "Onizuka Eikichi, 22 years old." before declaring his motivations to do something. "Onizuka Eikichi, 24 years old." In Paradise Lost.
Character Development: In Early Years he starts as a street punk, but as the battles continues he starts seeing that it's not worthy of his friends being hurt and on the verge of dying. That's when he starts thinking of giving up being a Yankee.
Chivalrous Pervert: He had plenty of occasions to have his way with some female students (like Urumi), but he still prefers to have consensual sex with somebody that really means something to him. Like Azusa.
Determinator: And how! Could easily turn into a Juggernaut. Heck, you can throw literally everything at this guy and he still wont be stopped. Not even a broken clotted blood vessel in his brain could keep him down for long.
Disappeared Dad: Eikichi's mother raised him alone, he never saw his father since several years.
Faking the Dead: Jumped from the top of a building with Ryuji to try and put an end to the endless gang fighting at the end of Early Years, it worked. However, their friends see throught the charade because they used a fake knife to stab eachother.
Jerk with a Heart of Gold: Less of a heart than usual examples, but unlike most teachers in the show, Onizuka cares deeply about the welfare of his students and will see to it that they become better people under his watchful eye.
Like Brother and Sister: With Fujisaki Shinomi, which annoy her to no end. Because of this, Onizuka never date her.
And according to Shinomi herself, this his how he views Urumi Kanzaki too, which annoy her as much as Shinomi.
Underestimating Badassery: ALL THE TIME in Early Years, bigger opponents understimate Onizuka because he's a 16 years old kid. Just ask Machida 
Unluckily Lucky: He's sometimes this. In one example from the anime, he comes across a large bag of money (that's good), which he spends all at once. It turns out the money was the school's field trip funds, which was planted on him in order to frame him for embezzling (that's bad). He somehow manages to convince the school not to fire him (that's good), but only by pledging an even more expensive field trip which he can't possibly afford (that's bad). He then fails to earn anything near the amount needed, only to win a car in an unrelated lottery (that's good). He then lends the car to a complete stranger, with no guarantees that the stranger will return it on time, if ever (that's bad). The stranger turns out to have been hired by the person trying to frame Onizuka (that's bad), but has a change of heart and returns the car anyway (that's good). At the last possible minute, naturally.
Would Hit a Girl: A variation. While he isn't the type to beat up girls, Eikichi doesn't go easy on females who cross the line, especially in the live action series where he didnt hesitate to punish Miyabi by holding her by the feet from a building's ledge until she apologized for bullying Noboru.
Best friend of Onizuka and the other member of the Onibaku Duo. Met Eikichi in High School, they started as enemies when Danma saw Onizuka's Ax-Crazy self beating someone to a pulp. He then wanted to anger Onizuka enough to see it again and fight him. They became friends since and he used to be The Lancer to Onizuka.After finding a girlfriend and moving to Tokyo, he took his family's bike business.
Get on his bad side and you're in for big trouble.
A Man Is Not a Virgin: Was in this as bad as Onizuka, first. Then he met Ayumi, then Nagisa and finally got his wish.
Bad Ass: He used to team up with Onizuka, so he's bound to be.
Faking the Dead: Jumped from the top of a building with Onizuka to try and put an end to the endless gang fighting at the end of Early Years, it worked. However, their friends see throught the charade because they used a fake knife to stab eachother.
Hot for Teacher: To Ayumi in Early Years. They both loved each other but she left him because she's way older than him.
Tender Tears: In Early Years, when his first love, Ayumi, his teacher ( 8 Years older than him. ) leave him after they got married. He's left in a broken mess, sobbing against Onizuka's chest.
You're Not My Father/Archnemesis Dad: When his father come to see him, Ryuji knows well enough his father never liked him. He tells him that straight.
Ryuji: As far as I'm concerned, my father might as well be dead.
It's worth mentioning that Ryuji ended up taking his family's bike business in GTO, so maybe they made up.
Teacher in Tsujido High School, where Onizuka and Damna are. She met Ryuji during summer vacations before they moved to Tsujido and she'll fall in love with him. After many trials she'll decide to date Ryuji. She has a troubled past ( Her boyfriend died in a bike crash a few years before, on chrismas day. ) She'll finally marry Ryuji, with just the two of them during a summer night before leaving him, finding unfair to rob him of all his teen years and friends.
Ryuji haves good tastes for women, indeed.
Dark and Troubled Past: Her boyfriend died on Xmas day in a bike crash, she have trouble dealing with the lost, even when she's with Ryuji.
Will They or Won't They?: They did kiss.They never had sex though, she left before and Ryuji backed out when he got the chance.
Ryuji's current girlfriend. She was the girlfriend of Akutsu, leader of 2nd Generation Midnight Angels. She was so scared of him and of everything he made her do that she created a litteral Split Personality named Yaksha to protect her from the trauma. Ryuji and Onizuka break the curse and she turns out to be a very cheerful girl. She lives with Ryuji in GTO.
Ryuji's wife, for real this time.
Bad Ass: Nagisa, somehow. But there's no doubt the devilish Yaksha is.
Former Rival of Onizuka during his delinquent times, Saejima was the kind of guy who would do anything to accomplish his goals. He destroyed the lower half of the last guy's face who challenged him, everyone was then scared shitless of him after that. A while after, he tried to challenge the Onibaku. He managed to force a good friend of Onizuka betray him but he was defeated anyway by Onizuka himself. 5 years later he became a cop. He makes cameos in GTO.
Anti-Hero: Type V. He is possibly the most corrupt and violent cop that can be found in any manga. However, at the end of day, he is still one of Onizuka's best, most trusted and loyal friends. If Onizuka somehow has to call for his help, he would be by his side until the end. Was still as crazy and violent before becoming a cop.
Ax-Crazy: Like a good deal of the Early Years villains, he was.
Still is. In fact, if you somehow manage to push Onizuka to the point of running to this guy for help, you are basically fucked. God has mercy, Onizuka knows mercy, HE DOESN'T!
Bad Ass: Being one of Onizuka's partners in crime in their early years, he kicks ass!
Seajima's former partner when he was a street punk. The other Kamakura's Wild Dog. Teamed up with Saejima against the Onibaku. He got beaten by Danma and became friend with him and Onizuka. He's most of them time a secondary character, but receive a lot of character development during the Natsu Return Arc ( told mostly from his point of view), dealing with his best friend supposed to be dead Natsu. He moves to the USA after that. He's a straight up guy but is not above fighting dirty if the situation calls for it.
Friend of Onizuka, Danma and all of the gang in Early Years. She met them in High School, she was the fat kid everything mocked. But she fell in love with Onizuka. Two years later she came into Onizuka's new High School after a big diet making her really beautiful. However, Onizuka did treat her very much the same way as before, with utmost respect, going as far as treating her like a sister. Which Shinomi hated since it ruined her chance to get with him. When Onizuka and Ryuji fakes their death at the end of Early Years, she's left heartbroken and doesn't appear in GTO at all. until GTO Shonan 14 days when Onizuka returns to Shonan and meet up with her again.
Eikichi, a teacher ? Yeah, right. Gimme a break.
Badass: Well, she was like a female Onizuka back then.
Formerly Fat: As hot as Shinomi is in Early Years and Shonan 14 Days, she was fat when Eikichi met her. After saving her from rape when she was 13, she fell in love with him. 2 years later she came back in the same High School as him, now smoking hot.
Legendary Leader of the Midnight Angels Gang, Senior of Onizuka and Danma. He first met them in Bad Company, a short gaiden published in Early Years' last volume.He died two years before Early Years started. Was rumored to be unbeatable in street fighting and in bike racing. Onizuka inherited his bike and coat, making him his successor.
The Cameo: He's a important part of Onizuka's story, but he only does cameos
Stepford Smiler: Initially behaves this way all the time towards her students in class, thinking it to be the only way to be a proper teacher, even as her female students hurl insults toward her. She eventually learns this is only hurting her, and that it's best to just open up and be herself.
Tsundere: B-type towards Onizuka. And he likes it!
The Runner Up Takes It All: Subverted. She was the true winner in the contest held in the anime, but only because all the postcards that were sent to her had her names covered up. In the manga, it's played straight. She didn't win, but most of the attention was on her after her amazing acting and improv, more so than the actual winner.
Urumi: I tried to seduce him, but he keeps ignoring it. He even payed me back earlier's dinner I gave him. It's so frustrating. You give him everything and you don't get anything back, not one bit of love. Maybe I'm just wasting my time.
Shinomi: It's not that he doesn't love you, you're like a little sister for him. Same for me, I tried everything. I went on a really big diet for him. It's been eight years already and nothing back.
Urumi: Eight YEARS ???
Double as a Call Back, since Eikichi viewed Shinomi very much the same way in Early Years.
Teens Are Monsters: She doesn't blink an eye on selling Miyabi's and her groups' virginity to save Onizuka's job to a groub of dirty old men with disturbing fetishes and she's alright with making a snake bit Onizuka's privates.
We Used to Be Friends: With Miyabi and Tomoko. Although she still gets along with the latter and despite everything, deep down she always considered Miyabi a friend.
Yandere: A serious enough case that she was ready to commit suicide if Onizuka didn't survive is aneurysm.
Humble Pie: Onizuka's approach to punish her, Naoko and Mayuko for bullying and humiliating Noboru involves tying them by their hands, spanking them (in the anime only) and take pictures of them butt-naked after letting Noburu write apologetic words on their ass (on their panties in the anime). He then uses said pictures to bargain them into giving up the ones they did of Noburu. Needless to say, this severely damages her pride.
Jerkass: Very much so. She really likes picking on people.
Karma Houdini: Remember that time she failed to seduce a teacher so she ruined his reputation instead?
Well, she does suffer a lot throughout GTO(resulting in 2 suicide attempts) which could be considered as her punishment, even though most of that suffering stems from her family's messed up situation, and alienation of her friends as a result of her bitchiness.
A better example of Miyabi being a Karma Houdini is probably the fact that even after Onizuka & her classmates come to know that she fabricated the whole molestation story, destroyed a teacher's life & led the whole class into an insane anti teacher campaign(which in turn destroyed the lives of at least 2 other teachers) based on that lie(not to mention the mean way in which she treats her classmates), she still gets their sympathies & full moral & emotional support.
Badass Teacher: She saved Daimon Misuzu from the school she set on fire.
Big Good: She saw Onizuka's potential as a teacher and gave him an interview after witnessing him having the beginnings of a true teacher. And she's also one of the few people on the teaching staff that have faith in him from the start, the other being Azusa and is always going out of her way to make sure Onizuka keeps his job.
Heel Realization: Later in the manga, around the end of the Teshigawara arc, he realizes that Onizuka really is a good teacher and he's the one who's failed as an educator.
Jade Coloured Glasses: What is arguably the saddest thing about him is that when he first started out as a teacher, he was every bit as idealistic about helping his students as Onizuka but 29 long years of working in the system had jaded him into what he is now.
Jerk Ass: Usually nasty tempered and deliberately unpleasant.
Jerk with a Heart of Gold: After his Heel Realization, he becomes (somewhat) more accepting of Onizuka's antics since he recognises that, at his core, Onizuka genuinely wants to help his students. While their dynamics don't ultimately change that much, during more serious moments he reveals the heart of gold such as during GTO: Shonan 14 days when Onizuka couldn't prevent a girl from the juvenile care centre being forcefully returned to her abusive mother, he buys Onizuka a drink and tells him a story about a similar thing that happened to him with one of his past students and a violent father ending with the student murdering the father during which he admits he regrets how he didn't intervene in the situation enough and his realisation of the limitations that teachers like him have in helping their students.
Knight Templar: He really wanted Onizuka out of school because of his delinquent appearance. And he doesn't feel at peace unless Onizuka is out, regardless of the good impact he was having on class 2-4.
My God, What Have I Done?: After Onizuka calls him out on being more concerned with his career than saving one of his students' lives and thinking of said student as a mere 1/400 of the student body, he realizes how far he drifted from his father's beliefs as an educator and realizes how far he's fallen.
Took a Level in Kindness: After his Heel Realization, he becomes much nicer to Onizuka, having around the same level of approval to his teaching methods as Sakurai does. The other times after that he's shown to be angry at Onizuka are much more justified (Namely, that Onizuka spiked his daughter's drink on a date and
Pyro Maniac: She set her school on fire! Though to be fair, she was also having a breakdown.
Best Served Cold: You have to give her points for all those planning and dedication to trying to bring down Director Sakurai.
Four Eyes, Zero Soul: At first. All she is concerned is her revenge and thinks of the students at school as nothing more than gears to move a business forward and believes school is nothing more than a business, the complete opposite of Sakurai. Then finding out that Sakurai saved her from the fire she caused and Onizuka saving her from a second fire kickstarted her Heel-Face Turn.