Eva Fins

Sometimes, a Mecha designer wants their work to look that much more impressive. The solution? Verticality. These go way past Shoulders of Doom in a very specific way, although they aren't necessarily pauldrons. Eva Fins are when a mecha has a pair of large fin-like projections from the back or shoulders that are far taller than they are wide, extending far above the head of the mech. They may serve a purpose aside from intimidation, such as being the equivalent of a vehicle roof-rack, but they may very well just be decorative.

Just to reiterate, these are separate from Shoulders of Doom. Eva Fins are characterized by giving the mech a very particular type of upper body silhouette, and do not need to be pauldrons.

Anime and Manga

 * Neon Genesis Evangelion, being the Trope Namer, has this in spades. All of the Eva units in the series, except Unit 00 before being refitted and have these. They serve a few different purposes, as they work as: knife holders, jump jets, spike cannons, mounting racks for additional batteries and other equipment, an anchoring point for connecting to the rails of the vertical launch tubes,.
 * Provisional Unit-05 uses them to mount pantographs which replace the umbilical cable while operating underground.
 * The actual script doesn't really have a consistent name for these, though the term "shoulder pylons" gets tossed around often as not.
 * As if lampshading their purpose as, virtually any change in the Evas will first involves the Eva Fins exploding. Such changes include Rebuild of Evangelion continues with the
 * Gun Buster, another series by Gainax, has this too in the eponymous mecha. in this case, they house rocket boosters and storage containers fot Buster Shield, Buster Tomahawk and Buster Homerun.
 * Mazinger Z: Although the titular Humongous Mecha itself had normal shoulder pads, several Mechanical Beasts had Eva Fins. One example is Baras K9, that had long and pointed shoulders were part of his Jet Pack. Many Warrior Beast from Great Mazinger and Vegan Saucers from UFO Robo Grendizer had Eva Fins. Grendizer itself had hints of this, sporting long, sharp, circular blades sprouting from his shoulders.
 * The Rick Dias mobile suits in Mobile Suit Zeta Gundam have large fins on their backs as well. for that matter, quite a few mobile suits in zeta (including the Gundam Mark II) have similar back-mounted fins or protrusions, although the only suit with similarly large fins is the Hyaku Shiki. in this case, they function as either extra "limbs" for zero-G maneuvering, or thruster mounts.
 * And the Rick Dias' successor in Mobile Suit Gundam ZZ, the Schuzrum Dias, takes this to ridiculous proportions. And in this case, the fins come mounted with cannons in addition to the standard thrusters.
 * The ν Gundam (Nu Gundam) has its funnels. The fact that they're called Fin Funnels only gives bonus points.
 * Present on the eponymous mecha of Space Runaway Ideon.
 * The SDF-1 Macross from Super Dimension Fortress Macross. It has fins that turn into a Wave Motion Gun.
 * And after their botched take-off attempt, the ship loses the conduits that power the gun; bypassing the missing section involves transforming the ship into humanoid form.
 * Both the Modified and Armored Valkyries feature auxiliary boosters that increase the vertical stature of their battroid modes. In "Do You Remember Love", the Modified Valkyrie's right booster has the fuel tank replaced with a "strike cannon" that is even taller (when it's not folded forward).
 * The Macross Quarter and the Macross-class Global research ship from Macross Frontier. In the former's case, the fins don't serve any specific purpose, as the vessel's Wave Motion Gun is a detachable Gunpod that the Transforming Mecha wields in its right hand.
 * they do serve a purpose on the Quarter, they're nacelles for the centerline engine thrusters
 * GaiGar from Gao Gai Gar has these. It's not clear in-show what they're supposed to be - extra maneuvering thrusters or guide rails for combining, maybe? In addition, GaiGar seems to have been designed with an EVA sensibility - humanoid and agile - which Gao Gai Gar throws out the window.
 * Verdant in Linebarrels of Iron has massive fin like pods on its back, their purpose? to hold the 20 swords verdant uses in combat, also serve as a physical shield and when they open up they give the blue mecha a very menacing winged appearance.
 * Non-mecha example: in Bleach Resurrecion have something between this and Giant Poofy Sleeves.
 * Taomon's attire from Digimon Tamers also has Eva Fin projections. They are only taller than Taomon if she removes her hat, though.
 * Skull Killer Jakiou, an earlier series about a berserker cannibal bio-mecha also has these.
 * Armada Megatron. Energon one too. And Star Saber from Victory.
 * The Raiden and Shinden mechs in Gasaraki have these; ostensibly they're the battery packs that provide the "Tactical Armors" with power. This hasn't helped certain accusations one bit.
 * The Jagd Mirage in The Five Star Stories with its Wave Motion Gun pack installed. There is a reason why they are nicknamed The Twin Towers. Namely, their barrels are 150 meters long, which boosts an already impressively tall (~50 m) Jagd's height to an obscene 200 meters.
 * In Tengen Toppa Gurren Lagann [Super Galaxy Gurren Lagann has giant drills mounted on its shoulders. When it performs a Giga Drill Breaker, they detach and connect together before attaching to the mecha's hand.
 * The Guren in Code Geass gains a pair of Fins when it is upgraded into the Guren S.E.I.T.E.N.. These Fins are more than decoration: they're actually slash harkens... not that it needs them when it can simply Rocket Punch enemies with a Wave Motion Gun. Still, Kallen likes to humiliate outclassed opponents with them, especially while delivering a Kirk Summation or Shut UP Hannibal
 * In Shaman King Asakura Hao has these when using an armor-type Over Soul.

Film

 * The Bayformers trilogy does this with car windows.

Live Action TV

 * TimeRobo Beta/Time Force Megazord, mode blue from Mirai Sentai Timeranger and Power Rangers Time Force has very high shoulders, especially on the toy. It should be noted that the shoulders/arms of this formation are legs in an alternate configuration.

Toys

 * Bionicle: normal Skrall and Mata Nui have these.
 * Transformers toys - Transformers Armada and Transformers Animated Megatron, to name a couple. G1 Optimus Prime had smokestacks to give this effect.

Tabletop Games

 * Sometimes shows up in Battle Tech, especially on mechs like the Awesome, which varies between little stubs above the arms to giant metal sheets extending above the mech's cockpit.
 * Eldar Wraith units and Titans in Warhammer 40k have wing-like protrusions sprouting from their upper backs that apparently serve as force-field generators.

Video Games

 * Geth Primes in Mass Effect have a fairly large set of these, which serve to draw attention to them. as if you needed any help figuring out which one was the Prime. Though in universe, these fins are apparently radio transmitters.
 * It's possible to get this look on your mech in Armored Core games, by mounting a pair of radar extenders. No real point though, as your sensor range will be boosted far beyond the range of any of your weapons and you'd be better off with at least one back weapon.
 * Weltall from Xenogears has these, though they point more backwards than upwards.
 * Not mecha, but Space Pirate commandoes in in Metroid Prime 2 have tall shoulder fins like this.
 * Justice, the queen and commander of the Gears from the Guilty Gear series has these, which add to her cyborg like appearence. In fact, her face when her mask plate is gone kinda looks like a berserk EVA unit. Hmm, coincidence.
 * The Mauler assault 'Mech from Battle Tech has two vertical missile launchers on its shoulders. The Phoenix Hawk also falls under this trope in the 'from the back' variety, and the Shiro boasts Eva Fins in the form of flags. The 'protrusions from the shoulders' category have representatives such as the Charger, the Griffin, and the Tiburon, all of whom boast added but not substantial vertical height.
 * The Armacham Ordog MCA from Shogo. Admittedly, its fins are angled back more than is usual for the trope, but they still reach above the head enough to fit.
 * The Terran Thor assault mech from Starcraft II boasts a set of four giant stacks coming off its back - they look useless until you order it to use its Strike Cannon ability - the whole mech hunches forward and the fins turn out to house 250mm cannon. There's also a special addition Thor that adds on several decorative fins.
 * The Protoss Colossus, while lacking shoulders, has several fin shaped aerials that could pass as Eva Fins
 * Zone Raiders in Command and Conquer 3: Kane's Wrath sport Eva Fins on their Power Armor. They hold rockets.

Western Animation

 * Shockwave and Megatron in Transformers Animated have this going on, as do Starscream and the rest of the G1 Seekers.
 * The original Jetfire and his Classics remake have this as well, owing to his Macross origins. And if Shockwave counts, then so does the original Ultra Magnus.
 * Soundwave in Transformers Prime.
 * Soundwave's can be justified as transformation kibble, since his arms form his wings in vehicle mode.
 * G1 Ultra Magnus has a pair of freaking girders growing out of his shoulders.
 * The Megas in Megas XLR has a pair of massive Cadillac-fins on either side of the head unit, courtesy of Coop.
 * The flashback episode of Generator Rex chronicling Rex joining Providence. Turns out he's got a Super Powered Evil Side that turns him into a Humongous Mecha with All His Shapeshifter Weapons Combined, including two Slam Cannons, shoulder-mounted in Eva Fin position.
 * Lex Luthor's giant mech in an episode of Justice League (Season 1). In fact, the mech itself looks like a thinly disguised Evangelion Unit 2. Possibly a Shout Out, since the series' creator Bruce Timm is a bit of an Evangelion fan (he's done a few Timm Style drawings of Evangelion characters).

Real Life

 * In feudal Japan, samurai sometimes wore flags on their back. See The Other Wiki. This might also be the original source of inspiration for Eva Fins