Soaperizing

A non-Soap Opera narrative with special interest in the relationships of the characters rather than their heroic exploits. This trope can apply to any work of fiction: a Vampire Detective Series, a Humongous Mecha Anime, a historical Thriller, or what-have-you. Movies and television which invent all-new superheroes quite often take this route (either that or they go the "realistic" route, without costumes). Usually it has a "softer" feel and much more screen time devoted to getting to know the characters and their individual strengths and foibles and on their "civilian" activities. Relationships change and develop over time, and much of the show's driving force comes not from plot but Melodrama simple interactions.

It's not uncommon for such series to "take a break" from the normal heroics to have an episode of pure characterization (Comic Book fans have long nicknamed these "baseball issues") or to eschew the heroics/doctoring/detecting entirely in favor of other soap opera staples like the Soap Wheel and Four Lines, All Waiting. In the case of soaperheroes superheroes, part of the drama will derive from separating hero and civilian identities with romantic complications. Anime beach episodes, when not entirely devoted to Fan Service, can be a form of this trope.

Anime

 * This is something often mentioned about Neon Genesis Evangelion - that it was unusual for a mecha series to be so focused on characters and interpersonal relationships. Maybe it's part of a broader trend?
 * Some would say yes. Eureka Seven's first half certainly thinks so, and the middle section of Rah Xephon also has these traits
 * Gundam Seed; to the point where it was practically formulaic to have one episode with action followed by an episode with nothing but soap.
 * A lot of Anime fit this description. Cardcaptor Sakura comes to mind, quite a few episodes of the Anime had no action at all.
 * Rozen Maiden. Given that this is pretty much a Moe series, it's not surprising.
 * Code Geass. In there with all that mecha fighting and political intrigue and overacting, they manage to squeeze in all sorts of high school drama and comedy, leading to sometimes-incredible Mood Whiplash.
 * Gunslinger Girl is somewhat like this.

Comic Books

 * Captain America tends to get all angsty about young sidekicks (particularly regarding Rick Jones) because Bucky "died" (Winter Soldier is a long story for another time) while his sidekick. This also explains his early animosity towards the Young Avengers. Similarly, Cap's own comic book made commentary on '40s vs. "modern" (whatever time period we're in) American values.
 * Peter Parker is the posterboy of this, apt considering he's probably the tropemaker.
 * Empowered and Ultra come to mind.
 * Noble Causes is a Soap Opera where the characters just happen to have super powers.
 * Runaways. Yes, the plot really is the driving force, but we wouldn't have the whole Nico/Karolina/Xavin subplot if it wasn't at all Soaperheroes.
 * Watchmen, although the theme seemed to be "costumed adventurers" didn't have any life outside of fighting crime.
 * Young Heroes in Love, a short-lived DC Comic.
 * Exemplified by Chris Claremont's early work on the X-Men.
 * Early?
 * Preacher (Comic Book) had long stretches where the story took a break from the overall Rage Against the Heavens plot to focus on the relationships between the three main characters. This is most evident in the arcs later collected in Dixie Fried and All Hell's a-Comin'.
 * Marvel Adventures: Avengers turned away from saving-the-world plots to focus more on filling up lazy afternoons with activities like showing up at a country fair, chasing down spammers, dating, and pestering each other. Maybe not melodrama so much as passing the time.
 * Plenty of Astro City stories are more character studies than they are superhero epics.
 * Incredible Hulk, especially in The Seventies and early Eighties.
 * Done regularly in Strikeforce Morituri, given the character-driven nature of the series.

Film

 * The Incredibles.
 * Sky High.
 * Parodied in The Specials. There is no actual super-combat or rescuing on screen at all.

Literature

 * Soon I Will Be Invincible.
 * Wild Cards, in places.
 * The third and fourth series of Warrior Cats have been described this way by fans, since there's really no antagonist and no overarching conflict (until partway through the fourth series).

Live Action TV

 * Soap of course.
 * Heroes, at first anyway. The third season so far seems to be focusing almost entirely on superheroics.
 * No Heroics is a British comedy about a group of four B-list superhero friends who hang out at a superhero pub. No heroics are ever seen onscreen, with petty larceny being far more common.
 * The pub specifically has a "No Powers" rule.
 * Also My Hero (TV). He performs heroics, but never on camera.
 * Star Trek the Next Generation, though it's usually Negative Space Wedgie Of The Week.
 * Battlestar Galactica Reimagined: Half of its plots revolve around interpersonal relationships, though they went overboard with it in the latter half of season two and third quarter of season three. They pulled a few superb conclusions to those seasons to make up for the dip in form luckily enough, and the show was at its best mixing genres and usually had the balance right.
 * Its prequel/spin-off series, Caprica, shifts even further in the direction of soap opera / family-based drama, while retaining a penchant for larger dramatic themes. The result is a very different show.
 * Stargate Universe is sometimes accused of this (and, tellingly, is also accused at times of being a Battlestar Galactica ripoff).
 * While The Tick was more of a sitcom-type then a soap-type, it rarely showed the superheroes fighting, instead throwing them in plots like "meeting new heroes in an abusive relationship" or "suing the magazine that displayed naked pictures of Captain Liberty".
 * 24. Whenever there's a couple real-time minutes to fill between Jack's latest action scene or torture technique? You can bet someone in either CTU in the White House be interrupting all their important business to talk about a coworker's feelings.
 * Lois and Clark: The New Adventures of Superman caught a lot of flack in its day for being more like "Moonlighting with superheroes" than other Superman shows, which were traditionally more action-oriented.
 * Though Smallville has always focused on interpersonal drama to a bit higher degree than, say, Superman the Animated Series, lately the story-to-sitting-around-wangsting balance has been tipped far in the wrong direction, even with Lana Put On a Bus for good (we hope.) With Green Arrow's He's Back moment, things may change, though.
 * Harpers Island uses this as a sort of Padding. Remember, your average slasher film is only about 90 minutes long; this one has some 13 hours to fill!
 * The complaint of soaperization was frequently levied at the US version of The Office, especially during season four and early season five (what with the drama over Jim and Pam and the Dwight-Angela-Andy Love Triangle).
 * Professional Wrestling has often been called "Soap Operas for guys."

Video Games

 * A Show Within a Show in City of Heroes is mentioned that's apparently a soap opera involving superhero characters, called The Super Days.
 * Techincally, this is part game mechanic for Shin Megami Tensei Persona 3 and Persona 4 as the player not only goes through an Action RPG with Dating Sim elements. And it's become a Cash Cow Franchise and brought Atlus into the mainstream english videogame market.

Web Comics

 * Super Stupor. In the words of the writer: 'It's about heroes and villains in their everyday lives. Really, that's it. '
 * Everyday Heroes. Truth, Justice, and Lawn Care.

Web Original

 * Interviewing Leather focuses primarily on the interview of the supervillainess rather than seeing her in action.

Western Animation

 * The Venture Brothers, though not precisely superheroes, a mix of Deconstruction, parody, soaperheroics and Dead Baby Comedy.