Cupid Hates Odd Couples

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When two friends or siblings fall in love with the same person, one of two things will happen.

If the show is an Afterschool Special or comedy, the friends will fight for a bit and then realize that what they are doing is stupid because "friendship is more important than some guy/girl". The guy/girl turning out to be a Handsome Lech or The Vamp is what usually makes the friends realize this.

If the show is aimed at an older audience, this Love Triangle will break when one steps aside and allows the other to have a chance at love. This preserves their friendship.

Examples of Cupid Hates Odd Couples include:

Anime, Light Novels, and Manga

Toradora!: Ami steps aside for Minori (even though she thinks the relationship wouldn't work) apart from little hints. Minori has been stepping aside for Taiga, who wasn't interested. Taiga steps aside for Minori when she does get interested. Taiga for Sumire, Yuusaku for Sumire's career. Everyone is just so generous, aren't they?
Clannad: Kyou's route is about this trope for her and Ryou, first with Tomoya starting to date Ryou basically to be a nice guy, not because of any interest. Then he realizes he doesn't really love her, and instead likes Kyou. But he could be happy with Ryou as well. Both of them realize this as well, and it just gets awkward. Tomoya eventually tries breaking up with Ryou, who runs away before hearing it. Then, she tells Kyou to cut her hair to look like hers and calls Tomoya to school, where he successfully breaks up with 'her' and admits he likes Kyou. To Kyou.
In the '90s anime (only) of Sailor Moon, both Usagi and Rei are interested in Mamoru. Rei steps aside, giving this children's show the more mature resolution to the situation.

Literature

Subverted in The Alien Series. Jeff and Christopher, cousins, both fall for the same woman. But neither steps aside for the other and the Love Triangle is resolved when the woman chooses one.

Live Action TV

This happened five times in Sister, Sister.
Drake and Josh: In the episode "Believe Me, Brother", Drake's girlfriend Susan falls for Josh.
On Angel, Wesley and Gunn both fell for Fred pretty much simultaniously. Fred chooses Gunn, which Wesley is none to happy about but grudgingly tolerates...until he's ejected from the group for taking Angel's infant son (though in Wes' defense, he was saving him from a rather gruesome prophecy that turned out to be false). One complicated reunion, breakup between Fred and Gunn, and half season of sexual tension later, Wesley finally gets his girl. That is, until she's possesed by a blue-haired demon and killed. Ah, the bliss of Joss Whedon.
In several episodes of Friends this is a central conflict theme between the characters. For example, in "The One with Mrs. Bing", Monica and Phoebe both happen to fall for the same guy... who happens to be in a coma... however, all true-conflict between the two is overcome when coma-guy resurfaces and ends up being a jerk (or just completely sane depending on your point of view).
In Degrassi, Emma and Manny both have a crush on Craig in season two. But when he shows signs of liking Manny more, Emma stops being interested in him because she doesn't want to compete with her friend.

Newspaper Comics

Flash Gordon: the Barin-Aura-Flash-Dale Love Quadrilateral finally breaks when Aura realizes she loves Barin after all (much to the relief of Flash, who had been loyal to Dale the whole time).

Opera

In The Pearl Fishers, neither guy gets the girl, and they patch up their friendship at the end.

Western Animation

Totally Spies!: All Three Amigos had a crush on David for two seasons. They spent his première episode bickering about it, and afterwards, without explanation, only one would pursue him an episode with either indifference or support from the others. They probably had an offscreen agreement to take turns.
Kim Possible: In "Exchange" (2x12), Kim and Monique fought for the love of some Japanese exchange student, until they eventually got over it for The Power of Friendship. Just to see him being hocked with Bonnie.
Total Drama Island: Both Trent and Cody are attracted to Gwen. When Cody finds out that Trent's the one Gwen likes, however, he not only steps aside, he actually helps them get together (with limited success, since Rule of Drama insists their romance be bumpy until the finale, but still). And then they break up the next season, giving Cody another chance. Which he loses. To Dun can. Unlike with Trent, this time Cody just punches him in the face.