In what is probably the most wide-spread example of this trope, the Touhou fanbase is, ostensibly, nothing but a GIGANTIC NAVAL WAR. Marisa Kirisame is probably the most disputed, having no less than 4 even divisions.
Most fans often have preferred ships but realize that in the world of Touhou, everyone belongs with everyone else. Fanworks often portray in-character ship wars as comedy. (IE Alice versus Patchouli for Marisa, Keine glaring at Mokou hanging out with Kaguya, and so on). Oh, and the whole mess with Marisa is parodied here (site NSFW).
Sheena/Lloyd vs. Colette/Lloyd in Tales of Symphonia fandom, with Sheloyd shippers arguing that Colette is too annoying, and Colloyd shippers arguing that Sheena is favored because of her Ms. Fanservice role.
Oddly enough, the Yaoi Fangirls don't do this as often. Key words: as often. You don't get between a Genis/Lloyd fan and Zelos/Lloyd fan if you value your brain cells.
Kratos/Anna and Kratos/Raine shippers were also pretty nasty to each other a few years back. And let's not get started on what Kratos/Yuan is to either of them...
There's quite a bit of animosity between fans of Sonic/Amy and Sonic/Sally. Somewhat odd because Sally and Amy mostly don't exist within the same series — Sally does not appear in the games or Sonic X, while Amy does not appear in Sonic SatAM. The only version of the franchise where both Amy and Sally exist is the Archie comic, in which Amy has a large hurdle to getting Sonic's attention — having a 10-year-old mind in a 15-year-old-body.
And then there are the fans who question Sonic's sexuality. Sonic/Amy vs. Sonic/Sally is nothing compared to the Sonadow (Sonic and Shadow) vs. other female character shipping.
It is not well known and the groups are not very big, but after the Sonic Rush series came out, there has been quite a few intense flame wars between Sonaze (Sonic/Blaze), Silvaze(Silver/Blaze), and Shadaze(Shadow/Blaze). Arguably,Sonaze is the most popular of the three due to the occasional teasing of the ship in various media, but that won't stop the 3 from going at each other.
The Baldur's Gate community, while small and generally quiet and civil on the subject, features an interesting and unusual take on Ship-To-Ship Combat, in that there's virtually no discussion, and a great deal of fan art and fan fic, many of which espouse one (or more) ships and ignore, or on a rare few occasions, publicly torpedo other ships. This is mainly because everyone except for the main character is an Optional Party Member.
In Mass Effect, Commander Shepard has a variety of love interests to choose from of both sexes (not that it stops people from shipping Shepard with non-canon options too). Each pairing has its supporters, and while most of them are "live and let live," there are certain sects that are vehemently against certain characters being paired with anyone else besides Shepard (namely, Garrus, Thane, Tali, and Liara). The fact that Garrus and Tali hook up in the third game—provided they were not romanced at all—only threw gasoline on some fires. And then there's the Joker/EDI and Joker/Shepard ship combat as well...
Mass Effect 3 ignited a firestorm of Shepard-centric ship warring, largely due to reduced screen time for the Mass Effect 2 love interests and the controversial way several of their storylines were wrapped upspoilers Jacob will leave you for another woman, Thane will succumb to his illness, and the only way to keep Kelly from getting killed is to convince her to change her name when that dialogue option is available.. Among Fem Shep die-hards, Shepard/Kaidan vs. Shepard/Garrus is probably the ugliest ship wars get in the fandom. In general, most Shepard-centric ship wars in the fandom seem to fall along the lines of humans vs. aliens, with accusations of favoritism by the writers across the board. Shipping is such Serious Business in Mass Effect fandom that a fan survey was created on it and sent to Bioware.
It may be a BioWare thing in general. Knights of the Old Republic has one official ship for a male Revan, two (a het and Gay Option) for female. Fans will either take them as a given, or spin off into other territories like F!Revan/Canderous. Jade Empire has a smaller fanfic base, but the Spirit Monk's romantic choices are mostly a non-issue, even with the Bi the Way status of Sky and Silk Fox. In the case of both Mass Effect and Dragon Age, BioWare, to varying degrees of success, attempts to not officially designate a character the 'proper' love interest—every player is free to choose who their love interest is, making any conflict inherently pointless.
The Dragon Age fandom, in fact, was relatively quiet on this front, with some minor exceptions (do not mention the Darkspawn Chronicles DLC if you value your life, and there's some backlash against Female!Cousland / Alistair simply because it's the most frequently shipped pairing). The second game, OTOH, has an ugly ship war going on between Hawke/Anders vs. Hawke/Fenris, which is fueled by the fact that the two characters represent the game's diametrically opposing views on mages, itself an endless hotbed of wank in the fandom. Hawke/Merrill is fairly safe, and Hawke/Isabela is also smooth sailing.
The Kingdom Hearts fandom, especially as of the second installment, seems to be comprised of two groups: those who regard shipping as Serious Business, and those that ship for fun or to point at and laugh at the first group. The introduction of Organization XIII basically just gave the former group license to spark flame wars over the relative merits of the #### ship of the day (12 males that hang out in a castle all day? Why, it's like shooting fish in a barrel!). Oh, and never mention AkuRoku if you value your head.
EVERY Final Fantasy game gets this, to some degree. There is a reason why OT 3 shippers are coming out of the wordwork for this series. In many cases, they're the fans who have grown sick of the shipping wars and who have decided to Take a Third Option.
Final Fantasy X-2: Back when the fandom was more active, there was something of a friendly rivaly between the Gippal/Rikku and Gippal/Baralai ships. That neither had any real canon support probably helped a lot.
Golden Sun: The wars between the four combinations coming from Isaac, Garet, Jenna, and Mia (just to clarify, I'm talking hetero pairings here) are kinda like a Mexican Standoff, except everyone is, well, shooting at each other. Heck, the four pairings from that one group could easily fuel debate for several years without touching the dozens of other pairings in the GS 'verse. However, a lot of the pairings are just for fun (Magmashipping, anyone?).
The third game is set to star the descendants of the heroes from the first two games. Things are already getting ugly.
One pairing has been confirmed canon, but its partner...seems to have been sunk. The first four playable characters each have a member of the first game's party for a parent, and none of them are siblings, which means that neither Isaac nor Garet ended up with Mia. However, Isaac x Jenna is canon.
Phoenix Wright: Ace Attorney: There's plenty of Phoenix/Edgeworth shipping and lots of Phoenix/Maya shipping, both of which are hostile to other ships (Phoenix/Iris for starters) and each other. Yaoi is one of the main common ships, the figurehead being P x E. If you don't ship that or instead ship a hetro that isn't P x M, you are totally in for a nightmare of harassment and ridicule. Also beware of Mia/Diego shippers, though most are friendly enough if you don't question the canonicity of their ship.
Combat is also going on between Edgeworth X Franziska and Edgeworth X Kay shippers in the Japanese fandom.
Go to any forum about The Legend of Zelda and you'll find ample discussion about which woman (or man) Link should end up with. Given that Link has no real personality but the player's, you have to wonder if shipping debates are more about which person the player wants to end up with.
Kyrie/Nero is hardly untouched. Perhaps a minority, but the Dante/Nero shippers can be quite vocal, especially if you so much as mention Kyrie.
Psychonauts has Sasha/Milla and Lilli/Raz versus Sasha/Raz and, occasionally, Lilli/Milla. Although this tends to consist of the former getting Squicked out at the latter and the latter making arguments as to why It's Not Gross.
Even before Aggra existed, there was already a bit of a ship war between Arthas/Jaina and Thrall/Jaina.
The Disgaea fandom fights over whether Laharl should end up with Etna or Flonne, or if the latter two end up with each other.
In the third game, Mao/Beryl VS Mao/Almaz fights are common.
Star Ocean: The Second Story has the Claude/Rena shippers at odds with the Dias/Rena shippers, with the Claude/Dias, Claude/Ashton and Dias/Ashton fans occasionally joining in. (Oddly enough, the various Yuri pairings, the het pairings that don't involve Rena, and pretty much any pairing involving Noel are ignored in shipping wars.)
In the Portal fandom, you've got Chelldos (Chell/ GLaDOS ) vs. Chelly (Chell/Wheatley) vs. Wheatdos (Glados/Wheatley). And that's just the main trio.
However, the "shipping war" aspect is generally absent, especially on the PortalKink Meme, where they even discussed what fun it might be to get into raging arguments about whether Chell should be with GLaDOS or Wheatley or neither while other posters tried to appeal for calm, but eventually decided it wouldn't as good as shipping their favourite couples, writing about them and tolerating others to ship and let ship.
Persona 2 has mostly the rabid Tatsuya/Jun shippers, who don't seem to take the existence of Tatsuya/Maya shippers kindly.
Persona 3 gives us all of Makoto/Minato/the MC's possible pairings, with Yukari Takeba getting the bigger pot shots (Double if it's from MC/Aigis or MC/Mitsuru shippers). If we go to the FemMC route, it's not wise to mention how Minako/Minami/Hamuko can get together with either Ken Amada or Shinjiro Aragaki; both pairings are known for rising HUGE hackles in the fandom.
On the forums, it's fairly common for posters to rank the routes/girls in their signatures with ">" or "=" signs. For example, Favorite>Second favorite>Tied for third=Tied for third>Least favorite
There is quite a significant number of people in the Halo fandom who point out that no relationships between Spartans can happen, but somehow there still seem to be fan pairings. John/Kelly, John/Cortana, John/Miranda, and John/Thel being the most dominant in the fandom. The first three are easily the most popular, but the last one seems to be growing at a snail's pace. John/Miranda supporters were not held back by the fact that Miranda died in Halo3, they just change the outcome of the battle to say that she survived. Really, none of these pairings could happen, because Spartans are engineered to have no sex drive. But the fans don't care.
A rather interesting case: Normally, Warship Gunner 2 is about warships blowing each other up. But the unlockable Special missions seem to intend to instill this idea - one of them is in fact an Escort Mission where you travel around sightseeing, and the three "love interests" (two men - one of whom is an old man - and a German doctor who is a looker in her own right) actually dig out naval fleets with the intention of blowing each other up over the Player. Fortunately you put a stop to this.
Surprisingly enough (especially for a game with one male and two female leads) Skies of Arcadia has almost none of this in its fandom. This is because the game neither sinks nor confirms the Vyse/Aika or Vyse/Fina pairings - and unmissable dialogue with each girl indicates that she is in love with Vyse, but completely accepting of the fact that he loves the other girl (and they both get along very well). The fandom has as such largely accepted the interpretation that the game is hinting at a Vyse/Aika/Fina One True Threesome.
Fans of Bang/Litchi and Litchi/Arakune fans are often seen battling around the Internet. Consequently, Bang/Litchi fans tend to also be Arakune haters.
Jin/Tsubaki fans often attack poor Noel, even though Jin/Noel was sunk in the port. Since Continuum Shift, Jin/Makoto is gaining popularity as a pairing, but conflicts between fans of the two pairings are rare. Chronophantasma may simply end up igniting a cold war, however. Oh, and there's a portion of the community who prefer to Take a Third Option and leave Jin as a Celibate Hero, instead supporting Hakumen/Tsubaki, causing more friction. Finally, we have fans of Jin and Mai Natsume, the protagonist of Blazblue: Heart Remix: a likely reasoning behind this is similarities between them and Ky/Dizzy.
Ragna is paired with practically everyone, but the most common pairings are Ragna/Rachel and Ragna/Noel. These two are the most aggressive of the fandoms, and battles wage constantly between the two. Not helped by the questionable nature of both pairings: on one hand, the age gap between Ragna and Rachel is ridiculous, and Rachel is a lolicon. On the other hand, the fact that Noel is a clone of Ragna's sister leaves a bitter taste in some people. What's worse, the game seems to hint at both.
The Fate/stay night fandom is divided between people who ship either Shirou/Saber, Shirou/Rin, or Shirou/Sakura. The former two pairings have the biggest fan followings, with the latter being the least popular of the three; perhaps not too surprisingly, the biggest ship wars seem to consist of Shirou/Sakura shippers arguing with Shirou/Rin and/or Shirou/Saber shippers.
Do not mention either Sumika or Meiya, or which would be better with Takeru on any forum or thread dedicated to Muv-Luv. And especially don't say the words "Noble Confidant". That is, provided you value your Brain Cells: It gets more violent than a BETA attack.
The King of Fighters fandom used to have very fierce ship wars in the second part of The Nineties, and sometimes these still pop out once in a while. Kyo Kusanagi x Iori Yagami is one of the most famous/infamous cases of slashy Foe Yayever in any videogame fandom, and whoever mentions Kyo's canon girlfriend Yuki or even hints that they ship Kyo with her... will likely be called "homophobe", "heterosexist" and/or "boring", with bonus "Yuki is a bland, antifeminist, Mary Sue-ish Damsel in Distress and a Take That to fangirls from the creators so SHE MUST DIEDIEDIE for the sake of both feminism and yaoi" cat-calls in between. The few Kyo/Yuki fans that are still around may react via passive-aggressively accusing ALL Kyo/Iori fans of being "canon breakers", "shallow", "bitchy", "self-loathing misogynists who fetishize men but bash women for 'not being strong enough'", and/or of supporting a pair where the two men hate each other without any traces of mutual respect without any other basis than 'they look hot'.
It's not much better whenever AthenaAsamiya, who's hinted to have a crush on Kyo in some continuities, is mentioned. Kyo/Athena fans will whip out the "Yuki is WEAK and ANTI-FEMINIST and DOES NOT UNDERSTAND KYO ENOUGH, so Athena DESERVES Kyo's affections better since she's more interesting, stronger and prettier" argument, while Kyo/Yuki fans will either repeat the aforementioned "hey don't be canon breakers, Kyo and Yuki haven't broken up for all we know" argument or ask "if you think Athena such a Strong Woman, why are you making her worth depend less on HER and more on whether Kyo finds her pretty or not?" This will get more complicated if Athena's Dogged Nice Guy Kensou is brought up: some Kensou/Athena fans will just support the idea of a possible "double date", while others will accuse Athena of being an "ungrateful bitch who doesn't appreciate Kensou" and/or "a shallow slut who throws herself at the feet of an already taken man while passing up the feelings of the guy who loves her and said taken man's girlfriend". (Nevermind that Athena is an Idol Singer as well as a fighter so she cannot go into datesand that she's totally dedicated to her career.)