The Dating Do Si Do is the tendency for a long running piece of fiction to recycle characters. In shows dealing with relationships especially, the tendency is that the longer the story goes on, the greater the likelihood that everyone will at some point have been in a relationship with (or at least slept with) everyone else. Well, usually not quite everyone, but still, the number of people having been in a relationship with other people is probably greater than could be expected under normal circumstances.
Usually it seems to be done to avoid introducing new characters. Unlike a Love Dodecahedron, a series that enjoys this dance does not necessarily have any of the couples being in competition with each other.
As can be noted, this is especially common in long-running series that still keeps a fairly regular cast.
Compare No Going Steady and No Loves Intersect.
Named after the Do-si-do, a figure in several dances that involve the dancers switching partners.
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Lots of comics have this to some degree, but the best example would have to be Spider-Man. All of Peter Parker's girlfriends (except Deb Whitman) have dated other members of his supporting cast at various points. Sometimes multiple members of said supporting cast. Spider-Man: The Animated Series rectified this oversight by adding some Will They or Won't They? between Deb and Flash Thompson.
Live Action TV
In your average Soap Opera it's hard enough trying to figure out the relationships happening at any given moment; you can safely assume that any character has been involved with 90% of the cast members of the appropriate sex at some point in the past.
In the reimagined Battlestar Galactica, most of the main characters go through a series of relationships with everyone else, sometimes at the same time. Lee and Kara stand out as particular offenders of the trope.
Played with in Friends. Almost all of the straight, non-incest pairings had a Ship Tease, though most were Played for Laughs, and almost all the characters have kissed each other. But only three pairs (Ross/Rachel, Monica/Chandler and Joey/Rachel) were treated seriously and actually happened. Given the show ran for ten years, the writers did pretty well at not having the characters constantly date each other.
Gossip Girl, complete with an actual chart on the Gossip Girl blog. Lampshaded whenever they have to explain it to someone new.
This is mostly averted in the Noah's Arc series, but played very straight in the movie with lot of sexual crossovers between Noah, Wade, Baby Gat, Chance, Ricky, Brandon, and Eddie (basically all the main characters except Alex).
On Sabrina the Teenage Witch Mr. Kraft dated both Hilda and Zelda at different times. Sure it's dramatic, but I'd hate to be in Sabrina's position on that one.
Popular, though it was a high school show and perhaps a Justified Trope. That said, boy, Josh did sure get to make out with/boink what, all the female cast short of April Tuna?
The L Word fits this one quite nicely, especially "The Chart", which basically kept track of all their partner switch-ups.
That '70s Show had a pretty tame version of this, mostly centering on how by the end of the show's run, Jackie dated three of the four young male regulars. More notable was the lampshading — see the page quote. The What If? episode makes it a little more complicated, revealing that Hyde would have started dating Donna if Eric hadn't kissed her at the end of the first episode.
Two Guys and a Girl (not to be confused with the trope with the same name) had this to the extreme in the final few seasons. Pete had gone through 3 girlfriends, fell in love with the eponymous "girl" Sharon, and had sex with Berg's mom and ex-girlfriend. To say nothing of the cavalcade of women Berg went through.
The third season's pilot even lampshades it: when Kurt and Rachel come to Emma holding hands, Emma tells them, "I thought this day would come. This is the only dating combination the glee club hasn't tried!"
Angel, like Buffy, is full of this. Cordelia was in love with Angel, slept with his son, and had some UST with Wesley back in their Buffy days. Fred had a crush on Angel, and dated Gunn and then Wesley (who had been sleeping with Lilah). Darla was Angel's sire and his lover for 200 years; Lindsey was briefly infatuated with Darla (possibly as a transference of his obsession with Angel), and was later a couple with Eve, who slept with Angel. Angel and Spike were both in love with Buffy, and both had been involved with Drusilla, and then there was that one time...
When a new person asks if they have a chart, Gunn responds "In the files. I'll get it for you later."
Israeli suspence-action-drama series HaShminiya (The Octette in English) has this. At one point, one of the character's older sister comments, "Is there any combination in the Octette you havenít tried yet?"
Bones: Angela and Hodgins dated, then Angela dated Wendell then she dated Hodgins again. Cam dated Booth (twice), who then eventually dated Bones. Cam eventually went on to date Arastoo. Off in their own little corner is Daisy and Sweets who dated for quite a long time, but weren't involved in anyone else (although Sweets was involved with other girls before Daisy, like April the fish girl).
This is the entire raison d'etre of Diesel Sweeties. Even Metal Steve, the cast virgin, got in on the action until his surprise marriage to Allie V.
In Batman Beyond, Dana is the only recurring character with only one love interest. Even her steady boyfriend wanders from time to time. Alpha Bitches Chelsea and Blade seem to have a new boyfriend every episode, frequently each other's previous flames. Nelson Nash also bounces between girlfriends more than once.
Total Drama World Tour: mostly consisting of Gwen, Duncan, Courtney, Alejandro, Heather, and possibly Tyler, Cody, and Sierra.
But considering the fact that the writer for Total Drama was the original writer for Degrassi The Next Generation, this shouldn't come as a surprise.
Archer: There are, mathematically, twenty-one ways the seven main characters (Sterling, Lana, Malory, Cyril, Cheryl/Carol, Pam, and Krieger) could pair off; of these, a third have actually happened. Lana, Cyril, Pam and Carol/Cheryl have each had half of the other six.
At some colleges (even stereotypically unsocial and nerdy ones) this can hold disturbingly true. Even if there are no social cliques, there will be sexual cliques. If you make this graph with math majors, they'll call them clusters.