Siblings...you gotta love them. I'll cover some sibling tropes later, but this by far is one love triangle where someone goes left when they should have gone right.
Now what I mean is..there are some cases where incest is involved and it's gross. The only love triangle that involves any types of incest off the top of my head is the Kaname/Yuki/Zero triangle from Vampire Knight....
Here are some examples of this lovely trope...also spoilers....
-X-Men: Lorna (aka Polaris) dated Scott (aka Cyclops) in the backstory, and his brother Alex (aka Havok) in the series' present.
-In Hamlet, Claudius murders his brother Hamlet Sr. and marries his brother's wife Gertrude a month later. It's heavily implied that she herself was in on the plot.
-The Legend of Korra, Bolin has a crush on Korra, while she has a crush on his older brother Mako, who likes her back but has trouble admitting it. For added confusion, Mako is dating another character, Asami. Ultimately, Mako and Korra hook up, until the end of season 2, when they decide to break up and stay as Just Friends.
-The Bible has a rather complicated example with Jacob, Rachel and Leah. Jacob fell madly in love with Rachel, and worked for her father/his uncle Laban for seven years in order to earn the right to marry her. However, in Rachel's society it was shameful for the younger daughter to be married first( why is beyond me), so (with some help from the very thick veils used at the time, as well as some alcohol) Laban switched Rachel out with Leah, with Jacob only finding out during the wedding night. Rachel and Laban then forced Jacob to work another seven years so he could marry Rachel for real. One can't help but wonder what poor Leah felt about this arrangement. (In a slightly unrelated note, this is why we have the tradition of the bride removing her veil in Western weddings.Making sure no one pulls that shit again.)
Now it doesn't have to be both siblings fighting for the affection of some rando. It can be a sister trying to seduce her sister( or brother's) significant other ( which is a dick move by the way). Or the brother trying to protect their platonic friend( though people think otherwise) from their sibling due to their reputation as a heart breakers. Hell it can even be Person C playing both siblings against each other, which again is a dick move.