Quote from Great
Harder question :
"Girl chose 2nd/other guy instead of the one she initially liked."
but not Shoujo or Josei genre.
It depends on what we mean for "the guy he initially liked", because for example Naru in Love Hina had a one-sided crush for Noriyasu Seta sensei, but he almost never appears in the story. I'd not say it's what you guys are asking though since it's pretty obvious from the start that that relationship is impossible.
More realistically, I'd say Toradora! fits.
Unless you're strictly referring to a shounen/seinen story told from a girl's point of view, in that case I can't think of anything.
What I like in Trivial Pursuit style. Pick your category: