Sniping
For those who are quickscoping/no scoping, if you double tap Y quickly, it actually centers the sniper rifle so your shot goes straight through the middle of your crosshairs (as it does not always do so when you no scope).


Reloads
If you get caught reloading a clip that isn't completely empty, and encounter an enemy, a quick double Y tap will cancel the reload and give you a chance at fighting back.


Search and Destroy
This one is probably my favorite reason for the Y double tap. When playing search, To ninja Defuse, To look dead or to make an awesome Game winning Killcam (GWK)


Showing OFF: Sometime people do it because it looks cool, or to show off.

I have done that and it seems to work sometimes. The YY in MW2 was the best.