Awesome Music: In the second season episode broadcast on Oct. 2, 1976, the musical guest was singer Joe Cocker. At one point, he started singing "Feelin' Alright". Then, for the second verse, he was joined by John Belushi...as Joe Cocker. The result was a highly memorable duet.
Channing Tatum's first time hosting (who actually was a stripper for a year before becoming an actor), the monologue especially. The only non-stripper bits people remember from this episode is the Newt Gingrich: Moon President cold opening and the Weekend Update segment with Kristen Wiig as Lana Del Rey trying to defend herself against claims that her performance on SNL was a disaster because of her atonal caterwauling and inability to move around.
Inverted in the monologue as Tatum (the stripper) remembers all of his customers (an allegedly religious woman named Denise, a married woman named Bridget [whom Tatum remembers as "Flithy Bridget" because of all the filthy things she would ask for], a man named Leslie [who ends up dying when Tatum uses his stripper moves to refresh his memory], and Leslie's doctor, Dr. Matthews), much to their chagrin.
The episode hosted by Alec Baldwin and his wife at the time Kim Basinger on February 12, 1994 will forever be remembered as the episode that had the "Canteen Boy Gets Molested" sketch (and the episode after that, hosted by Martin Lawrence, will be remembered for Martin's raunchy monologue about women's hygiene [which was so tasteless, it nearly got everyone on the show fired and is often cut in reruns and replaced with title cards explaining the gist of the monologue and why it can't be shown on TV anymore]).
Likewise (for a nonsexual example) for the Tim Robbins episode from season 18, which was the notorious episode in which Sinéad O'Connor rips Pope John Paul II's photo and screams, "Fight the real enemy!"
Then again, that's probably not so much fanservice-y as it is controversial.
Every season after the first five years has a Broken Base (save for the seasons that were universally bad — season 6, season 11 note though it does have some fans, if only for Dennis Miller as Weekend Update anchor, and much like season 6, is viewed today as "It sucks, but it's not as bad as everyone else says.", and season 20).
There is a common misconception that Steve Martin (one of SNL's most frequent hosts) was a cast member. He was on Lorne Michaels' failed ABC sketch show The New Show, but he was never an SNL cast member.
Tina Fey's monologue begins with her saying she is excited to do all of her characters, but she she then says didn't have any. She actually had three original characters and some celebrity impressions she did twice
For Dick Ebersol, Eddie Murphy was his pet Up to Eleven, and he wasn't shy about letting you know that. SNL was basically the Eddie Murphy Show from Season 7 to 9 (until Murphy left). After that it became the Billy Crystal / Christopher Guest / Martin Short show. Ebersole definitely thought in terms of "This person/people are the lead(s), and everyone else is backup."
The Cast Showoff: There have been past cast members who have proved that they can do more than just funny characters and spot-on celebrity impressions:
Garrett Morris was a talented singer who would occasionally get to sing classical music on the show. One segment featured Morris singing a Schubert aria whle captions rolled on the screen explaining that the show only let him sing because everyone was scared of him.
Charles Rocket from the Jean Doumanian era was an accordion player (on the Season Six premiere, there was a sketch where he played a deranged man who killed his dates with accordion music, only to get killed by bagpipe players) and an actual news anchor (making Rocket the first and, so far, only Weekend Update anchor who actually had experience as an actual news anchor).
Maya Rudolph has shown off her singing ability (she was in a band prior to being on SNL and had parents who were involved in the music industry; her mom, Minnie Riperton, is best known for the hit song, and famous high note, "Lovin' You", a song conceived as a lullaby for baby Maya).
Fred Armisen is another cast member who has shown he has music ability (plays drums and guitar, though whenever he played Liberace, he faked playing the piano).
A. Whitney Brown (a writer-cum-feature player from 1985 to 1991 who often appeared on Weekend Update's "The Big Picture" segment) can juggle, as seen in this video, a talent he picked up while doing time in a Texas prison.
Jason Sudeikis was a basketball player for the University of Kansas, so that scene on the LeBron James episode from Season 33 where he plays a boom mike operator who challenges James to a game of basketball was just an excuse for Jason to show off his moves.
More recently, the Chris Hemsworth episode allowed Cecily Strong to show some considerable pipes in the "Sing Along" sketch.
Harpo Does Something Funny: Defied. Improvising is a good way to find yourself banned from the show by Lorne Michaels if you're a guest (unless something really goes wrong and you have to do something to keep the dead air at bay). Just ask Adrien Brody (who introduced musical guest Sean Paul while dressed as a rudeboy and rambling in a Jamaican accent when he hosted during the penultimate episode of season 28note 2002-2003).
Damon Wayans had a rather dull part as a prison guard in a "Mr. Monopoly" sketch (based on the game). He decided to ad-lib and play the character as a gay stereotype (who sounded like his Blaine Edwards character from the "Men on Film" sketches). He was immediately fired by Lorne Michaels, which is why he was available when In Living Color! premiered.
Internet Backdraft: Donald Trump's appearance as host during his 2016 Presidential campaign suffered from a great deal of backlash. Before the episode even aired, NBC took a lot of fire for seemingly flip-flopping on Trump after they very publicly cut ties with him months earlier. An activist organization offered viewers of the live performance $5,000 to heckle Trump by yelling out "you're a racist" on-air. And finally, after the episode aired, complaints abounded that Trump was only on the episode for 14 minutes, and his appearances were just extended campaign commercials (particularly one sketch where the entire joke was "things went well under President Trump").
Just Here for Godzilla: Most people who watch the show only watch it just to see one thing (be it a favorite sketch/recurring character/cast member/favorite host) and cite it as the main reason to watch the show. Weekend Update is commonly cited as the best example of this, since the simplicity of the sketch means it can be consistent even as the rest of the show wobbles.
Nostalgia Filter: As noted on the main page, those who grew up with the show are among the most vocal critics of its current shape. Also, because 60-minute cable reruns and video compilations have trimmed a lot of the weaker material from the older shows, it's easy to forget that even during its good seasons SNL had bad moments (from lousy hosts and musical guests to recurring characters and sketches that suffer from being underdeveloped and/or annoying — though this can apply to the stuff that people actually remember or have currently seen). The DVD box sets of uncut and complete seasons of the show, in the original order and from the beginning, may be helping to undercut this.
Pandering to the Base: When Bill Hader hosted the show in 2014, a new Puppetry 101 skit with his puppet Tony was done, as Bill had appeared on Howard Stern's show shortly before that episode, and Stern told him that the previous skit with Tony was his favorite of all time. Bill even hinted that Tony may make a comeback when he hosts, and even said if he did, people could thank Howard Stern for it.
The Scrappy: Colin Jost, one of the current Weekend Update anchors. Unlike the other cast members, he only appears in Weekend Update and has drawn numerous criticism for being wooden and unfunny. When it was announced that the show was changing Weekend Update for the 40th season, people were thrilled...until it was revealed that they were removing Ensemble Darkhorse Cecily Strong from the desk and keeping Jost.
Seasonal Rot: Just like in the Nostalgia Filter entry, there are former fans who believe the show hasn't been the same since whenever the last time they saw it — usually, it's Seasons 1-5 (Fall 1975 to Spring 1980), but there have been other claims of when SNL started to seasonally rot, like when a fan favorite cast member (such as Dan Aykroyd, John Belushi, Eddie Murphy, Will Ferrell, Tina Fey, etc.) leaves. The transitional periods between old casts and new ones are usually low periods, with Season 6 (1980-81), the first without any original cast members, widely considered the most disastrous in the show's history. Season 20 (1994-95) is also infamous due to the departure of Phil Hartman, reports of backstage tension between cast members, and the weak ideas for sketches (most of them were about the O.J. Simpson murder trial).
Season 11 (when Lorne Michaels came back and tried to assemble a cast of semi-famous people to be cast members, only to almost get canned due to plummeting Nielsen ratings) from 1985-86 also counts. According to the book "Live From New York: The Uncensored History of Saturday Night Live", a lot of the staff (including Al Franken and then-future The Simpsons writer George Meyer) view Season 11 as terrible because the first episode hosted by Madonna wasn't well-received, which led to plummeting ratings and reviews stating that SNL's new cast at the time wasn't funny, the writing was too weird and thin, and the show as a whole has run its course and needed to end.
Season 35 is an unusual example in that it wasn't seen as too bad while airing, but several years later, the writing does seem very unusual and geared towards certain cast members (usually Fred Armisen and Kristen Wiig). Some other seasons are usually seen as of low quality as well, such as seasons 28 (due to Jimmy Fallon's constant cracking up and the absence of Will Ferrell), 30 (had very mediocre political sketches during the 2004 election, the Ashlee Simpson lip-synching fiasco had people asking if the show was even live anymore, and everything just seemed kinda slow and dull. The upside of season 30 was that Tina Fey and Amy Poehler did a good job on Weekend Update), 33 (but only because the Writers Guild strike caused a lot of potentially good episodes to go unwritten), season 38 (the Justin BieberValentine's Day Episode, too much reliance on Bill Hader and Fred Armisen), and (to some extent) season 39 (criticism for not having a more ethnically diverse cast, the sketch-writing quality is too unbalanced, pretaped sketches seem to dominate over the live ones, absence of Bill Hader and Fred Armisen, too many new cast members who aren't seasoned to be on the shownote though Kyle Mooney, Beck Bennett, Noel Wells, and Sasheer Zamata have been commended for their performances. John Milhiser is slowly improving, Colin Jost just started as a Weekend Update anchor, and not that many people care much for Mike O'Brien or Brooks Wheelan, though Brooks is starting to be featured more in sketches and not just as a background character. Basically, if a fan-favorite cast member leaves, then the show will go through what's called a "rebuilding season," which means that the show's humor quality will either be mixed to in the toilet. See "They Changed It, Now It Sucks" below.
Special Effects Failure: SNL has always been known for flimsy sets, cheap costumes, and obvious Stock Footage (Lorne Michaels even said on an E! special about SNL's history that the show had this problem), especially in the 1970s and 1980s episodes (not so much in the episodes of the 1990s, the 2000s, and the 20-Teens, but it does crop up occasionally). More recent seasons have occasionally added in bad Chroma Keying as well. Some sketches have used this and ended with the cheap set getting destroyed in some way.
They Changed It, Now It Sucks: The near-constant changing of writers and cast members is one of the most common reasons why fans have a love/hate relationship with the show.
We're Still Relevant, Dammit: Considering the series is 40 years old and its heyday is long LOOOONG passed it's no surprise that they'll latch onto whatever the Topic of the Month is. Ghostbusters (2016), Ferguson, Drawing the Prophet Muhammad, etc etc etc.
What Do You Mean, It Wasn't Made on Drugs?: A lot of SNL's sketches from the 1970s were drug-influenced (such as one that had an Abraham Lincoln portrait calling Richard Nixon a "dip.") and a lot of the writers and cast members at the time were high as kites. These days, the writers and cast members aren't like their 1970s counterparts (at worst, they get high from sleep deprivation in writing and planning the show; at best, some of the cast and crew members smoke weed, but only in their off-hours), but there are some crazy sketches and characters that seem like they're the product of a drug-influenced mind (Toonces, The Cat Who Can Drive a Car, Will Ferrell's impression of Harry Caray, Bill Hader's Stefonnote who is heavily implied to be on cocaine, meth, prescription pills, and possibly ecstacy, according to Bill Hader, just to name a few).
The Woobie: Willie, Kenan Thompson's recurring character on Weekend Update. His whole shtick is recounting horrific memories of his life to Michael Che, his neighbor. And yet, he never once complains about them and is always so undyingly optimistic that you just want to give the guy a hug. Also counts as an Iron Woobie.