While there's half a dozen girls after Tenchi Masaki in Tenchi Muyo!, the relationship map stabilizes relatively quickly with six girls chasing Tenchi. Until Tenchi in Tokyo, which introduces Sakuya Kumashiro into the equation. She's probably one of the biggest examples of the Die for Our Ship effect relating to this. Though she eventually succeeds in winning Tenchi, she doesn't survive to the end of the series.
The third OVA introduces Noike who shows up already arranged to be married to Tenchi by a very powerful matriach of the Jurai royal family. Ryoko and Ayeka are not amused. Fan reaction, oddly enough, is less extreme than what Sakuya faced, but that's probably because the third OVA seems to get even more Fanon Discontinuity than Tenchi In Tokyo (the latter being treated as relatively more acceptable because it's just an alternate universe anyway).
In the 11th volume of the Sorcerer Hunters manga, Carrot fell into a serious relationship with a girl named Mousse, leading Chocolat and Tira to confront him with their true feelings. However, it turns out Mousse wasn't even real (?) and the plot turned out to be a set-up for the epic Final Battle in which Carrot eventually chose Tira.
Bleach has Senna from Memories of Nobody. By the end though, Ichigo/Rukia shippers and Ichigo/Orihime shippers can rest easy.
On the canon side, another potential choice is Tatsuki Arisawa, a childhood friend of Ichigo's and Orihime's best friend. She has little effect on the overall plot, but she has had a few Ship Tease moments with Ichigo. The other most popular secondary love option is the arrancar Nel, who's quite affection toward Ichigo (though there's a good chance that's just because she's a touchy-feely person, not necessarily because she's romantically interested in him).
A rather marginal example, as well as a subversion, pops up in Elfen Lied with manga-only Nozomi, who provides a third alternative of a girl who has feelings for the male lead Kouta that isnt Yuka or Nyuu/Lucy/Kaede. It's ultimately Averted in the anime (as she's not even included there!) and subverted as per the manga's rather... messy ending.
Mana Kirishima from the Girlfriend of Steel game. She has an unusual amount of hate directed at her, when you consider that she's a Canon Foreigner who barely even appears anywhere outside of her own game.
The Rebuild films, having embraced the fandom as it is, gives us this with new 3rd female pilot, Mari Makanami. An almost hybrid of Asuka and Rei, combining the positives and removing the negatives. She's only had about 10 minutes of screentime in the films so far, but that hasn't stopped shippers from tossing her with Shinji based on that alone. Though to be fair, Shinji is the only character she actually interacted with that wasn't an Angel.
The first two seasons of Zero No Tsukaima saw a wide variety of love interests for Saito, but by the end of season two it was pretty much narrowed down to Louise and Siesta. Enter Tiffania. Louise's reaction in particular could be heard from space. And then Tiffania was pushed to the back and replaced by Princess Henrietta, whereupon both Louise and Siesta were simply dumbfounded and stricken with worry: Louise had a Heroic BSOD and Siesta finicked about how she could easily remove all opposition and be alone with him.
Ukyo Kuonji in Ranma ½. Until her arrival, the primary contenders for Ranma's affection had been Akane (Betty) and Shampoo (Veronica). Although she never escaped Unlucky Childhood Friend status, Ukyo was still a relatively plausible third option and remains a popular choice in the fandom; she's even hit with Die for Our Shipless often than Akane and Shampoo are, in direct contrast to the common trend of the third option getting hit by the hardest with Die for Our Ship.
Watanuki's feelings for Yuuko and the pairing itself is becoming more and more canon. Especially after chapter 193, where Haruka pretty much comes out and has a heart-to-heart talk with Watanuki, giving him a relationship-advice pep talk ( "If you truly believe you and she will meet again, then you mustn't do anything that will make her cry."). Which prompts Watanuki to go into one of his melancholy worshiping moods of Yuuko, holding her pipe and saying her name.
In the SHUFFLE! anime the main character, Rin Tsuchimi is being pursued by Lisianthus (Gods) and Nerine (Demons), and his childhood friend Kaede. Who does he fall in love with in the end? The close buddy and tease, Asa.
In the Kimagure Orange Road manga, Sayuri Hirose attempts to be the third option for Hikaru's Betty and Madoka's Veronica. The catch is she means nothing to Kyousuke, so her attempts to seduce him were unsuccessful.
Athena in Hayate the Combat Butler. Hayate openly admits that he likes her, and several of the other girls reactions are shown as they either accept it or decide to keep trying. Even Nagi puts her trust in Hayate to do the right thing by abandoning her fortune and disinheriting herself, giving a strong feeling sense of incoming resolution. But it's a subversion because she leaves at the end of the arc, leaving us with the original unrequited love dodecahedron.
Although she was the last (officially) introduced to the viewers, she's actually the first girl that Hayate'd met, and she had appeared in flashbacks before Hinagiku had officially entered the harem.
Um.. by her own words, Hinagiku entered the harem on her first appearing, she just hadn't realized it yet. By Maria's wordings, she knew Hina would enter it before her first appearance. Athena has also reentered the harem officially as of ch 300.
Athena is probably Hata's vision of the Third Option Love Interest for fans, since the fandom was generally split between Nagi and Hinagiku, and she's taken from both of the Ships.
Post-Golden week chapters have given us Chiharu's entrance into the harem and potentially Luka/Ruka, who would actually fill this slot well, since we didn't even know about her existence until Golden Week had ended.
In Air Gear, the love interests Ringo (the Betty), and Simca (the Veronica), (and Akito) for Ikki were shaken up by the arrival of Kururu. Ultimately averted: Ikki chooses his Betty — Ringo.
There's also Kazu. When all three girls (Simca, Ringo & Kururu) find out a way how Kogarasumaru can still participate in the Glam Scale tournament they all hasten to tell Ikki about it thinking 'whoever manages to tell him first will secure their future at Ikki's side'. So, who's the one who gets to tell Ikki first? Kazu, of course! It's played for laughs but it does make one wonder...
He's a speed freak, so it only makes sense that he would beet the girls.
Axis Powers Hetalia: Russia's part of a canon Psychotic Love Triangle, harboring Mad Love for Lithuania and being chased by his sisterBelarus, but he also seems to display some interest in his southern neighbor China in a couple of strips (if "putting on a panda suit and stalking him" or "inviting him to live at his house in a very creepy way" can be considered Ship Tease, which it probably can given Russia'snature). Many fans happily take this third option, especially given the two countries' extensive real-life history together, to the point where Russia/China is actually more popular than Russia/Lithuania and Belarus/Russia combined. Russia gets plenty of other love interests in fanworks, of course, but China is the one who has the most canon support after Lithuania and Belarus (even if he probably isn't very happy about it in canon).
Also, in regards to England's "love life", we have America, Japan and France. Then Himaruya reveals that he's working on sketches for Portugal. Cue to fangirls latching onto Portugal and hoping they become this in one, two, three...
But Wait, There's More!India has entered the fray as well, having been one of the more important English colonies in the past. While the fandom tends to pair him up with Prussia due to their Bollywood dancing scene that's easy to see as a Dance of Romance, some people have also added him to England's list of possible love interests...
Although less popular, she also playfully flirts with Ukraine in a bonus strip in the fourth volume.
Korea himself might find the way into this too. As even though he groped Japan and China, he does take interest in Taiwan and is surprisingly nice to her. To summarize, both are actually the third option for each other, considering Taiwan's own share of ship tease also related to China and Japan...
Spain, who's mostly trapped between chosing Romano and Belgium, has to option of being paired off "rather" easily with Netherlands. The bonus is in form of Ship Mates that shipped of Romano and Belgium sweetly.
In Vandread, romantic tension is developing between Hibiki and his three love interests, and then in the second season a Girl in a Box shows up and decides he's cute.
Vivian Wong is this in the fifth season of Yu-Gi-Oh!. There is an intense rivalry over Yugi by his close friend Anzu, who cares for Yugi a lot but is mostly interested in the Pharaoh and the aggressive Bratty Half-Pint Rebecca who is quick to shower him with affection. When Vivian starts trying to shoehorn in, Rebecca and Tea are quick to unite against her, including Tea cheering Rebecca on in her duel against Vivian.
Qawool from El Hazard: The Alternative World. The male lead, Makoto, has already chosen his girlfriend ( Ifurita) and has other girls still chasing after him (Shayla and Nanami), but when Qawool meets up with him, she immediately snags a spot in his harem. Incidentally, she's also The Scrappy for other reasons, so the Die for Our Ship gets especially toxic.
Cheryl Blossom of Archie Comics, the character in the page picture and the former Trope Namer. She was a bombshell redhead introduced in the '80s who saw the original Betty and Veronica going after Archie and decided it would be fun to show them up. She makes her big debut in the 90s in the Love Showdown storyline, where Betty and Veronica escalate their competition for Archie, which ends in Archie choosing Cheryl Blossom instead (although the Status Quo is restored in a follow-up special). Since then, however, she has apparently started going out with the nerd of the cast after getting to know him on the internet, in a Throw the Dog a Bone moment.
Cheryl is also shown as being in the way of Reggie too. A humorous issue shows her winning a talent contest (with Archie and Reggie as the judges) over Betty and Veronica. What'd she do? Batted her eyelashes at them.
In what is a hilarious and awesome example, when the '90s Supergirl goes to an alternative Earth to take the original Silver Age Supergirl's place (it's long and complicated, but awesome), she ends up marrying the original Superman. In the wedding splash panel, you can see Lois Lane and Lana Lang saying "Please oh please — let it be a hoax! Or a dream! Or an imaginary tale!"
And Lori Lemaris, a friggin' mermaid, was Supes' original third option winner.
For a time in the 80s, Cat Grant was definitely in the running. Lacking any L's in her name probably doomed her.
Early in The Amazing Spider-Man Betty Brant (brunette) and Liz Allan (blonde) are competing for Peter Parker. Then Aunt May introduces them to her best friend's niece, Mary Jane Watson. They are both aghast at the thought of having to compete with this knockout beauty. Mary Jane's face is only shown several issues later, but fitting in with this trope, she turns out to be a redhead.
Occasionally, Black Cat is played as the third option to the other loves of Peter's life, MJ and Gwen.
Ultimate Spider-Man for a time went with this trope; at the end of Ultimatum arc in Ultimate Spider-man, Kitty accidentally revealed to MJ that she still had romantic feelings for Peter. 6 months of unresolved plot development, Peter was now in a romantic relationship with Gwen Stacy. It didn't last.
With Batman this tends to happen. Usually torn between Catwoman and Talia al Ghul, writers have recently decided to add Wonder Woman to the mix, although Batman doesn't like to acknowledge it. Sometimes.
In the Disgaeanovels, Laharl is given a rather big harem of girls as the novel series goes on, but Flonne and Etna are his closest friends and therefore his primal love interests, and he is not all that fond of the rest. But in the 3th novel we are introduced to Ozonne, Flonne’s little sister, and she & Laharl hit it off pretty well.
In the Gone series, over the first three books there were hints at a possible love triangle between Quinn, Lana and Edilio. In Plague Sanjit and Lana become a couple.
And in Lies, Edilio and the Artful Roger become a couple.
Live Action Television
Many fans felt that Nina filled this role on Angel. Of course, Cordelia was MIA at the time and Buffy was busy with her own series...but when has that ever stopped anyone?
Series 3 of Robin Hood had the title character in a Love Triangle with outlaw Kate (Betty) and villainess Isabella (Veronica). If you're wondering where his traditional love interest Marian is, she'd been Killed Off for Real at the end of the previous series, and became the third option when Robin also dies and is reunited with her in the afterlife.
Kurt from Glee spent most of season one deluded that he was a mix this trope and Gay Option to Finn. He wasn't. Then again, Kurt hooked up with Blaine...
It is revealed by the end of season 2 that he has been secretly seeing Britta but they break up once others find out about it.
In season 2 Annie still has feelings (including a lot of resentment) towards Jeff but there are hints that she and Troy might get closer. In the season finale Abed becomes a third option out of the blue.
Season 3 seems to run with this pairing, however. From the episode "Remedial Chaos Theory" onward, the show hints that Annie and Jeff are being groomed to be the Official Couple of the show, with Troy and Britta paired together concurrently.
During Season 7 of Degrassi we had the love triangle of Holly J (Veronica) and Mia (Betty) going after Sav. The two girls brutally tear into each other for Sav's attentions, finally leading to Mia thinking Sav picked her... until it turns out he likes Anya.
On Gossip Girl, Colin was this to the Dan-Serena-Nate triangle.
Also, fans were crazy in Season 4 to know who Blair would pick - Chuck(Vanessa) or Dan (Betty)? Turns out she picks Louis. No one was happy.
In What I Like About You, Holly leaves for England, while Vince(Veronica) and Henry(Betty) both expect her to choose one of them. She comes back from England with a new guy, Ben. Henry eventually moves on and goes to Princeton and Holly ends up with Vince.
In the ballet Rodeo, the Cowgirl and the Rancher's Daughter are both in love with the Head Wrangler, who in turn is interested in the Rancher's Daughter. During the final movement, "Hoedown," the Cowgirl gets the Head Wrangler's attention—but instead winds up with the Champion Roper, leaving the Head Wrangler and Rancher's Daughter to pair up.
The Enhanced Edition of Baldur's Gate introduces the half-elf wild mage Neera as the fourth romantical option for the male protagonist.
It also includes Dorn Il-Khan, a male half orc Blackguard. Overlaps with gay option, though the women can romance him too
In Tales Of Legendia, the two women who were fighting over Senel most aggressively were Shirley and Chloe. Unfortunately for them, it's revealed that the one Senel loved was Shirley's dead sister, Stella.
Tiltyu in Fire Emblem: Geneaology of the Holy War could easily be this for Prince Levin: Serious, honorable Fury and flirty, clingy dancer Sylvia compete for Levin's affections (well, Sylvia does most of the competing), but the player can easily push them aside and pair him with Tiltyu, a girl with no prior plot connections to him. Fury's Cool Big Sis Mahyna could have also been this if she'd survived.
A male example would be Arden for Ayra; Lex and Holin both have canon crushes on her, but Arden is her third predestined lover even if she never speaks to him outside their chapter five love talk.
Lachesis has... two of these, actually. Her most "canon" love interests are Fin and Beowulf, to the point that in Thracia 776 her son Delmud is Beo's kid and her youngest Nanna is Fin's child. However, if she gets enough love points with either Dew or Noish, she can have love talks with them as well.
Fire Emblem: Awakening has this, depending on your interpretation. Sumia is Betty and Maribelle is Veronica to Chrom. Sully, a female avatar, or Olivia may be seen as the Third, fourth, and fifth option love interests for him. Olivia may be the best example, since her being married to Chrom is a hilarious case of Strangled by the Red String. (Which becomes heavily lampshaded in-game.)
If the player restores the deleted romance with Neeshka in Neverwinter Nights 2, Safiya can become the third option with Elanee as Betty and Neeshka as Veronica. Similarly, if you restored the deleted romance with Bishop, Gann becomes the third with Casavir as Betty and Bishop as Veronica.
The DS version of Dragon Quest V introduces Debora, who functions both as this and as the 'Veronica' to Bianca and Nera's Betties. After showing no interest in the hero's actions or his completion of the Engagement Challenge he completed in order to possibly marry her sister, and turning an indifferent eye upon Bianca's entrance into the equation, she breezes in and offers herself as a third option at the last possible moment — although, naturally, she views herself as the ONLY real choice. (Even her dad is surprised at this! But not displeased, since he'd previously resigned himself to never being able to get anybody to marry Debora.)
In .hack//G.U., Haseo can romance almost any character, though the two canon options would probably be Atoli (Betty) and Shino (Veronica). However, play your cards right, and Endrance, who is a dude, will win Haseo's heart, much to the chagrin of every female in the party.
There's also Alkaid who is unlike Shino or Atoli in that she's firey and agreesive. While she and Haseo are initially at each others throats, they warm up to each much much faster than Haseo does with the other two, probably because Alkaid doesn't have psychological issues like them and is actually able to communicate effectively.
It's possible for Tatsuya to either romance Maya (Betty) or Lisa (Veronica) in Persona 2: Innocent Sin. However, it is also possible for him to start a homosexual romance with Jun.
In Subterranean Animism, those playing as Marisa had to choose between the two biggest contenders of her harem (in fanon, at least) Alice and Patchouli...and Nitori, a character that had only been introduced the previous game and had little, if any, connections with Marisa prior.
In Dragon Age: Origins, men have their choice of Leliana (Betty) or Morrigan (Veronica), with Zevran overlapping with the gay option. For women, he's the Veronica to Alistair's Betty, and Leliana serves as the third option.
In Bittersweet Candy Bowl, both Lucy and Tess were love interests for Paulo, but he ended up choosing Jasmine, a girl introduced at the last minute.
Homestuck has this with Vriska, who had romantic feelings for Kanaya, Tavros, and plausibly Terezi. She ends up asking John out, and dying before hearing a response. On the other hand, due to her species' romantic customs, she could have plausibly ended up with all of them in different quadrants..
Whateley Universe example: Thunderbird has all four of Sizzle, Aztecka, Tesla, and Widget interested in him for almost a year. They all lose out when Chaka realizes Thunderbird is a total 'boy scout' type and snaps him up in about ten minutes.