So, in Captain America: Winter Soldier, the Internet had a conniption when Black Widow showed up with this necklace.
Everybody thought this meant that Widow and Hawkeye were together. But we found out in Age of Ultron that ol' Clint is married with children. So none of that hanky-panky.
But then I saw this necklace in the Captain America: Civil War trailer:
It appears to be a green stone. Perhaps signifying her unrequited love for Bruce Banner, a.k.a. The Hulk? Or she really did hook up with Bruce since he's now rumored to be in Civil War?