Aragorn from Lord of the Rings, Tanis from Dragonlance, Drizzdt from Icewind Dale, Eragorn in the Inheritence cycle, Spock in Star Trek, Cecil and Aerith in Final Fantasy are the most famous, but I've also noticed it's not necessarily just half-elves that are big; come to think of it half-race characters are common in all fantasy. See, Med'an in Warcraft if you want to extend, Torres in Star Trek, Michael from Stargate, Darth Maul from Star Wars, and so on.
Is this just a trope played to give a character more potential back story and possible choices in a plot?