The original series, or the overall franchise, contains:
Anvilicious: Zig-zagged. The show, especially in Seasons 1 and 2, was very topical - addressing issues such as racism, alcoholism, drug abuse, etc. in a somewhat After School Special-like manner. In some episodes, these issues were handled very well. In others... to call them heavy-handed would be a massive understatement.
Ass Pull: The revelation of Jack McKay's survival in Season 10, despite the fact that he was blown up seven seasons earlier.
Awesome Music: The theme song! Or, at least, the two versions used from Season 2 onward.
Kelly, for her former reputation as the school slut, being an Alpha Bitch (though with Hidden Depths), and also the biggest reason, stealing Dylan while Brenda was away in Paris with Donna, which caused a major rift in the base. However, there are fans who believed Kelly improved over the seasons, became more of the Lovable Alpha Bitch, and it also helped a bit that she has a Trauma Conga Line (e.g. raped, nearly burned to death, suffering a miscarriage, getting addicted to coke, involved in a cult), which made fans sympathetic towards Kelly. Heck, she has fans with Grant Show (Jake from Melrose Place), Jason Priestley (Brandon), and Sara Foster (Jen).
Dylan. Even though he is also the Breakout Character of the show, he did tend to act like a major Jerkass to both Brenda and Kelly when he was in relationships with them. It didn't help that he was often the loner who felt that he had to deal with everything alone, especially prominent in Season 5 when he lost his fortune, often rejecting the help of his friends even when they offered. However, his fans also stated that his Freudian Excuse of a con-artist dad and a New-Age hippy mom justifies his behavior, and also believe that he is genuinely kindhearted, well-read, and generous when he strips away all of his stoic armor.
Bizarro Episode: The Time Has Come Today in Season 4. In the episode, Brenda finds a journal in the floorboards of her room; the book was written by a girl who lived in the house during the '60s who was having friendship issues around the same time as the Vietnam War. Brenda connects with the girl because she too is also at a rough spot with her friends at the time, and then goes on to imagine the girl Wendy and her friends as her and her friends. It's an odd episode because none of the characters look right as a '60s character (e.g. Steve in a Nehru jacket or Dylan as your typical hippie), and is basically an excuse for the writers to belt out their feelings about the Vietnam War, which none of the show's audience wouldn't really connect with. Also counts as Contrived Coincidence and Plot Parallel.
Growing the Beard: The first season included different filming styles, the theme song was odd when compared to the iconic theme (it was arranged in a dance-pop '80s style track, instead of the hard rock number that fans associate the show with today), several of the characters were no more than glorified extras (e.g. Donna) and also Scott Scanlon was a main character, despite given little to do. Also, the show was more of having a conflict-solution that could be solved in an hour. Because the ratings for Season 1 were poor, the producers sought for more change. They changed the theme, dropped Scott (permanently), elevated David and Donna's statuses in the cast, and the filming style was more soap-operatic than plain drama, reflecting the show's shift to season-long storylines with occasional very special episodes peppered in. It also helped that the producers also aired Season 2 during the summer, when most primetime shows were off the air. Needless to stay, the ratings increased and Beverly Hills, 90210 gradually became a cultural phenomenon.
Kelly: For her issues with her mom and dad, losing her virginity to a Jerk Jock who left her and spread rumors about her, her rape, her near-death experience in a fire, her miscarriage, her involvement in a cult, and so on and so forth.
Valerie: She hed been raped by her father for years ( which led to her killing him in self-defense), had turbulent friendships and romances, her mother once disowned her because she believed that she was willingly sleeping with her dad and even tried to blame her for everything that happened to Val's dad.
Narm: Not as extreme as the show's numerous parodies might have you believe, but it certainly has more than a few moments of this. The Sentimental Music Cue often used to underscore dramatic scenes certainly doesn't help matters.
Nightmare Fuel: The conclusion of "Up In Flames". Aside from being one of everyone's greatest fears, the scene of Kelly and Allison trapped behind the encroaching flames, screaming for the firemen to hurry up and get to them, is truly terrifying.
Most of the original teen characters were in their junior year in Season 1. However, they were still in that grade for Season 2. The producers decided to extend the lifespan of the then-fledgling show by retconning the characters' ages, except for David, who was already a year younger than them.
The death of Valerie's father was retconned several times. Initially presented as a sudden suicide, Valerie later admitted she killed him in self-defense when he tried to rape her; then it was revealed that she straight up murdered him without provocation (aside from the aforementioned rape).
Jack McKay's death is a major retcon, since his car was shown blowing up with no apparent way of escaping. Season 10 retcons this with Jack having survived, and entered the Witness Protection Program in the aftermath of it all.
Matthew Perry appeared as a one-shot character in the episode "April Is The Cruelest Month". He would go on to play his famous role as Chandler Bing three years later.
Vivica A. Fox, before her breakthrough role in Independence Day appeared in "Ashes to Ashes". Also Eugene Byrd, who portrays squintern Clark Edison on Bones, appeared as Fox's on-screen brother in the same episode.
Paul Johannson, before One Tree Hill, itself a show about teens who looked in their 20's and...had problems.
In the new series: Stephen Amell played a presumed dead guy who returns after being lost at sea. One year later, he plays the same type of character as his breakthrough role, Oliver Queen on Arrow.
Seasonal Rot: Same as Broken Base above, some fans believed that after Season 3, the show's quality started to decline, though others believed the show increased in quality after the characters graduated.
Strangled by the Red String: Emily and Brandon have a brief, unconsummated relationship that ends after she slips him Ectasy, resulting in her stalking and harassing him for several weeks after. Several years later, he tells Brenda she was the love of his life, despite the fact that he explicitly told her that he didn't love her when rebuffing her attempts at reconciliation.
Strawman Has a Point: More like "Strawman Is Absolutely Right", with a little Designated Villain and Unintentionally Unsympathetic thrown in in the infamous "Donna Martin Graduates" storyline. The school administration explicitly warns the students that having or consuming alcohol at the prom is strictly forbidden and that anyone breaking this rule will be suspended, barred from graduation activities, and have to attend summer school. So Donna gets drunk, gets the punishment. . . and we're supposed to feel sorry for her and see the administration as the bad guys? Um, no.
Donna's mother Felice was also frequently portrayed as an overbearing bitch, and she was portrayed this way again during this storyline. But she has every right to be angry at the parents who served her underage daughter alcohol and at Donna herself, who drank the champagne.
Tear Jerker: Brenda learning that Dylan cheated with Kelly (Season 3's "Back in the High Life Again"). Even though Brenda knew Dylan had an affair with someone during the summer, she didn't know who with. When Kelly revealed that she was the one, it was the ultimate betrayal. Brenda losing her boyfriend to a person whom she thought she could trust, which could easily connect with viewers who had a similar experience, and also goes to show that betrayal is never at the hands of your enemies. It doesn't help that Dylan acts very blase about it, though Kelly tries to soften the blow, though Shannen Doherty's performance speaks volumes.
Kelly: Neither of us wanted to hurt you.
Brenda: You didn't care how I felt at all, Kelly!
Brenda: Look, I hate you both. Never talk to me again!
After the death of Dylan's father, Brenda puts aside her anger to invite Dylan to stay with the family so that he won't be alone.
Brenda: Years from now, your dad will still be gone and I'll just be some girl you knew in high school. Dylan: (tearfully) No, you won't, Brenda. Not after everything. (They hug, and Dylan's remorse for hurting her and relief that she's beginning to forgive him is palpable)
Andrea remained a virgin longer than most of the other characters, but immediately when becoming sexually active she became pregnant, giving birth to a premature daughter who nearly died, having little support from her parents when she decided to marry Jesse.
Dylan had a con artist dad and a runaway New Age hippy mom, was The Alcoholic and a drug addict prone to relapses, his dad was killed in a bombing in front of him (though this was later retconned), he lost his fortune to his father's ex-mistress who then took her daughter (Dylan's half-sister) to Brazil, he lived homeless for a while, and lost his wife in a drive-by shooting meant for him, ordered by the woman's father.
David was dealing with a womanizing dad, a not-so-there mom, and recurrent drug problems.
Donna had drug problems, parental issues, domestic violence by her boyfriend, nearly got raped, was stalked and held up at gunpoint, and witnessed her father's death from a heart attack.
Gina in her final appearance at least, where everyone blames her for Dr. Martin's death from a heart attack, though she was simply just there when it happened. Even Mrs. Martin insinuated that her very existence placed a strain on his heart, which caused his death. Luckily, everyone realized their mistake after Gina did the eulogy for Donna when she couldn't do it.
The sequel series contains:
Ass Pull: Silver's cancer diagnosis in the series finale, the episode after she had a miscarriage.
Complete Monster: Douglas Atherton is a wanted rapist from England. He comes to America, renames himself Miles Cannon, and becomes a teacher to find new victims. At the end of season 2 he rapes Naomi Clark, even telling her that because she lied about him sexually harassing her earlier, no one will believe her about her rape. After he is found out, he flees his apartment, only to confront Naomi later and threaten her with a knife.
Creator's Pet: Annie could be considered this, particularly in the earlier seasons. In season 1, Naomi told Annie she would be uncomfortable with her dating Ethan since he was Naomi's ex. So what happens? Annie dates Ethan behind Naomi's back. The writers then expected the audience to feel sorry for her when Naomi hooks up with one of Annie's exes at her Sweet Sixteen party. The majority of fans sided with Naomi instead. Annie's Pet status continued into season 2 when she took the ENTIRE season to confess to her hit and run, but ends up only being put on house arrest for a couple of months (again, we're expected to sympathize). During that time, some fans even criticized Shenae Grimes, when Grimes was just doing her job. By the later half of season 3, the Annie hatred started to die down due to her screen time being cut significantly.
Ironically, it was Naomi who became this in later seasons. She continued to get focus even though she usually made things worse for everyone.
Crowning Momentof Heartwarming: More of a meta example but the "90210 4Ever" retrospective that aired after the last episode showed how close the cast had become. Unlike the Gossip Girl retrospective, the cast do their interviews in twos or threes, allowing them to laugh and banter with each other; Shenae Grimes and AnnaLynne McCord spend most of their shared interview holding hands. They also pass around a phone specifically made for "90210 selfies". Unlike many other specials of this kind, it doesn't feel fake and you can really see that the cast had fun making this show.
A canon version with Riley's death paving the way for Annie and Liam to get back together.
This was actually not the case with the fans. While they didn't like him for dating Annie, they really didn't have anything against him.
Ensemble Darkhorse: Mark. At least, people who comment on him consider him one of the most interesting minor characters, and have shown that they want him to appear more - maybe that's why he still is.
Fan-Preferred Couple: Annie and Liam have become this. It's weird because they experienced Foe Yay in Season 1, became friends in Season 2, started dating in Season 3 with a few breakups in between and broke up in Season 4 and fans want them back together. Against all odds, they overcome this and ascend to Official Couple.
Foe Yay: Annie and Liam in Season 1. It fades over time and long before they actually start dating.
Arguably Annie and Naomi in Season 1 and 2.
Naomi and Austin are a canon version.
Growing the Beard: Season 1 was considered a by-the-numbers teen drama, resulting in mixed reviews (though its ratings were actually the highest when compared to later seasons). Season 2 however saw less original main characters, the departure of Ethan, increased writing quality, and more added fun, which continued into season 3.
Season 4 and 5, however, are considered lower in quality because of its elevated melodrama, Flanderization of certain characters, backstabs galore, and too much focus on several relationships, including the Liam/Annie shippers. It doesn't help that the series finale had an Ass Pull with Silver's cancer diagnosis.
Hilarious in Hindsight: In Season One Naomi says if she were a lesbian, she would date Adrianna. In season 2, a lesbian does date Adrianna.
Also in Season One, George played Kellan Lutz is on the Lacrosse team. Lutz would later star in a movie about Lacrosse called "A Warrior's Heart".
Harry gave his son up for adoption and later adopted Dixon, who is black. In Season 5, it's revealed Harry's grandchildren from said son are half-black.
In the fourth season, Liam's friend Jim, played by Stephen Amell returns from being lost at sea.
Magnificent Bitch: Both Naomi and Annie have shown shades of this, Annie probably from hanging out with Naomi.
Moral Event Horizon: Many fans feel that Adrianna is irredeemable at this point. After switching out Silver's medication for Bipolar Disorder with placebos, it's going to be very hard to make Adrianna likable ever again.
Nightmare Fuel: Naomi's rape at the end of season 2. Especially Harsher in Hindsight, when in 2014, Naomi's actress AnnaLynne McCord revealed that she was sexually assaulted by a friend when she was a teenager.
Rescued from the Scrappy Heap: Annie dating Liam is what got the fans to finally accept her before she eventually became the most popular character on the show.
Retcon: Silver's age. She was born at the start of the original show's third season (1992) yet graduated with the class of 2011. With summer birthdays, students usually graduate before their 18th birthdays, though Silver would've had hers before the beginning of season 3 (her senior year), instead of season 4 (college freshman year).
They Wasted a Perfectly Good Plot: They should have shown Adrianna's mom while she was dating Gia, based on Maeve Quinlan's other role. Even if she was completely supportive of it it could have been a great contrast