Pairing: Mazaki Anzu/Kawai Shizuka, known to fans as Sideshipping.
Spoilers: The ending of the series, a fairly significant plot point involving Yami Yuugi, minor relationship spoilers.
Warnings: F/F pairing.
The Sweetest Thing: An Anzu/Shizuka Manifesto
Kawai Shizuka: Shizuka is the sweet younger sister of Jounouchi Katsuya, one of the main characters. Shizuka is girly, polite and quite timid most of the time, but she's capable of being brave when it counts and is willing to risk herself to keep those she cares for -- especially her older brother, whom she adores -- safe and happy. Otogi Ryuuji and Honda Hiroto both pursue Shizuka's affections, but she doesn't seem interested in either of them as anything more than a friend.
Mazaki Anzu: Anzu is the series' main female character and childhood friend of the protagonist, Mutou Yuugi, who has a crush on her. Anzu herself seems more romantically interested in Yuugi's "other self," the spirit who lives in his puzzle, normally called Yami Yuugi by fans and "the other Yuugi/the other me" by the Yuugiou characters themselves. Some fans dislike Anzu because of her "friendship speeches" and/or obsession with Yami Yuugi; however, friendship is an important theme in Yuugiou and Anzu's support is often the thing that gives her friends, especially Yuugi, the courage to go on when they need it most.
Are they compatible?
There's no denying that in canon, Anzu and Shizuka get along pretty well to say the least. Surrounded by boys as well as Kujaku Mai and Isis Ishtar (who are quite nice but also much older than Shizuka and Anzu), it seems only natural that Anzu and Shizuka, each being the only other female around remotely near the other's age, would become fast friends. But is there any room for them to become more? How do their personalities fit together?
In some ways, Anzu and Shizuka's personalities are very different. Anzu is bold, confident, determined (being the only character in the series to have actually planned a future for herself and taken steps toward achieving it), outspoken and tomboyish, as well as demanding, bossy and occasionally argumentative with an unfortunate tendency to drift off into daydreams or let her crush on Yami Yuugi overwhelm her common sense, especially in the early manga, while Shizuka is kind, understanding and generally more grounded than Anzu, but lacks the older girl's drive and self-esteem. Shizuka also seems to require reassurance from those around her, especially Jounouchi, whereas Anzu knows she's worth something and doesn't need her loved ones to tell her so. Anzu is outgoing; Shizuka is more introverted. Anzu has big dreams for the future; Shizuka just wants to focus on the here and now.
On the other hand, the girls are very similar in some ways, too. Both are courageous, strong in their own way and loyal to the very end. Both value those close to them, are optimists and are cheerful most of the time. Both are intelligent -- not geniuses, but at least relatively smart; Shizuka seems gullible and a bit dense where other people's motives are concerned, but we get the impression that this is because Shizuka is immature and sheltered, not because she's stupid. Anzu and Shizuka also seem fundamentally normal in ways a lot of the other characters in the series can't really be; they aren't fully "normal" because they're connected to the world of Duel Monsters because of their loved ones, but they are still more outside of the game than a lot of the other characters, and indeed, their primary focuses don't seem to be Duel Monsters. Anzu's focus is her love of dance and her desire to get to New York; Shizuka's, her family and her brother. Should they ever want to talk to someone whose life doesn't revolve around Ancient Egypt or a card game, well, they've always got each other.
I also motion that Anzu and Shizuka have similar senses of humor, which is always an asset in a relationship. While I wouldn't call either a girl a stand-up comedienne in training, they're frequently giggling together and they seem to find the same things funny (and the same things not funny or annoying). People who have different senses of humor can still have a successful relationship, of course, but sometimes it helps if the person you love likes to laugh at the same things you do.
The way Anzu and Shizuka fit together, as either friends or lovers, is compelling. They seem to make each other whole, fill the gaps in each other's lives. Shizuka needs someone who won't mind reassuring her, someone strong and protective but not overwhelming, someone who's willing to be there for her when the chips are down and she's doubting her self-worth, and most of all, someone she can trust. Anzu is all of these things, and she even seems to "tone down" her bossiness and overbearingness around more timid types like Yuugi and Shizuka. But what, then, does Anzu need?
Well, given Anzu's canonical romantic interest(s), Yuugi and the other Yuugi, what she needs is a combination of sweet and supportive, grounded and realistic, someone quiet and a little shy who's still capable of playing the hero. Anzu romanticizes being rescued, it seems, although she's perfectly capable of rescuing herself and would certainly not want to be treated like a mere damsel in distress. Shizuka, at first glance, does not seem to be the kind of person who would play the hero. She seems instead the type who might need rescuing -- which she does, on occasion. But she jumps into the ocean to save her brother Jounouchi from drowning and she stands up to Kaiba Seto when she wants him to land the blimp for Bakura Ryou, who's gravely injured. Indeed, polite, timid Shizuka is capable of standing up to people when her loved ones are at stake.
Anzu could reassure Shizuka day-to-day, could protect her from those who might hurt or take advantage of her, could make her laugh and smile, and generally be the kind of lover and companion that Shizuka needs, and Shizuka, in turn, could provide Anzu with both the constant, unyeilding background support that Anzu herself provides for so many others as well as someone who's willing to stick up for her when Anzu needs it most. Shizuka could also drag Anzu back to common sense and reality when Anzu is getting carried away; although Shizuka fanonically often has her head in the clouds, she doesn't strike me as particularly spacey in canon (dense in some areas because she's so young and sheltered, perhaps, but not spacey or the type to get carried away by fantasies).
In light of all this, I'd say yes, they're compatible. Compatible and so damn cute together.
Obstacles in the relationship?
The biggest obstacle from Shizuka's end is her brother Jounouchi, who's overprotective and looking to throttle anyone who looks at his baby sister's great gams. Of course, what tough guy in his right mind would hit a girl? So Anzu might get a break in that regard. That's not to say Jounouchi would wholeheartedly approve of their relationship, though given what he seems to want most for Shizuka is her happiness, he would probably eventually give in and stop arguing against anything that might occur between Anzu and Shizuka.
Otogi and Honda's obvious crushes on Shizuka could also be presented as an obstacle, but given that there's no indication that she likes them back, it doesn't seem like a very big one. We don't really know who Shizuka likes, assuming she likes anyone at all right now. (Canonically, she probably doesn't like anyone, but hey, we can always pretend she likes Anzu, right? And since it's never exactly refuted outright or anything...)
Anzu, on the other hand... well. Yuugi definitely likes her. She definitely likes Yami Yuugi, and there are hints that Anzu might have some romantic feeling for Yuugi, too. While Yami Yuugi loves Anzu dearly as a friend (much to the dismay of Anzu-bashers everywhere), there doesn't seem to be much indication that he has the same kinds of feelings for her that she has for him. Still, Anzu's interest in Yami Yuugi presents quite a few problems for the Anzu/Shizuka ship. For one thing, it proves that Anzu has at least some interest in boys, whereas Shizuka could be a closet lesbian for all we know. Of course, one crush doesn't mean that Anzu must be wholly heterosexual, since varying degrees of bisexuality do exist. However, while Anzu's sexual orientation isn't much of an issue, the fact that she sometimes seems downright obsessed with the other Yuugi is. How could Anzu ever move on from him? She's got her heart set on him, after all.
But Anzu does start to move on from Yami Yuugi, slowly outgrowing her crush and hero-worship and becoming more mature in her way of viewing romance as the series progresses, and at the series' end, she'll have to move on from him completely, since he disappears. Anzu is a strong girl and not the kind of person to languish in a lost love for very long. Of course, normative Yuugi himself also presents an obstacle, and he's still around. Also, while Anzu doesn't seem to return his crush on her at first, later on in the series we get hints that Anzu likes normal Yuugi as well as the other Yuugi. But then, Yuugi himself states in the manga that he could never really love Anzu like that because of her hero worship of Atemu (Atemu is Yami Yuugi's true name), and even if Anzu and Yuugi did hook up, there's no telling how long the relationship would last. You don't always marry your high school sweetheart, after all.
While I don't dislike Yuugi/Anzu, I think that an Anzu/Shizuka 'ship might be better for Anzu in the long run since, while Shizuka is similar to Yuugi in all the ways that matter, she's also different enough that she could be her own, distinct person in Anzu's mind, and not just a constant reminder of Yami Yuugi.
So, yes, there are obstacles to Shizuka/Anzu, but nothing that can't be worked around.
Unfortunately, there's precious little art or fic for this pairing (or any Yu-Gi-Oh! shoujo-ai pairings at all, for that matter), but I've managed to scrape together some recs that I think are worth checking out:
Carry on Dancing by The Angst Junkie/darth. A cute little drabble about Anzu and Shizuka at a high school dance.
Strawberries by samurai-ashes/cheeky_duckie. Another cute little drabble, this one about eating strawberries.
Behind the Roses by Misura/misura. Another short, cute drabble, in which Shizuka confesses.
If anyone has anything they'd like to me to add to this short list, please comment.
All screenshots used for this manifesto came from this site.