How do I get rid of Zenyatta's Orb of Discord?
Solution 1:
As the other answers have said, killing the Zenyatta removes the orb, as does Recalling with Tracer or going invulnerable as Reaper (Wraith Form) or Mei (Cryo-Freeze).
Additionally, Zarya's Projected Barrier and the personal Barrier both remove the Discord Orb, as far as I know. You can call out to an allied Zarya or play her yourself to remove it.
This one is the most situational, but using Self-Destruct on D. Va, getting your mech killed, or calling down a mech, will remove the discord orb from you.
LOS'ing the Zenyatta is the most effective and reliable strategy, however.
Solution 2:
According to the wiki,
The orb of discord returns after 3 seconds if not in vision.
So to get rid of it, you can run out of his line of sight for 3 seconds. Alternatively dying also removes the orb of discord, but is somewhat counter-productive. Also, if you kill the Zenyatta, the orb will go away, though it can be risky since you will take extra damage while fighting him.
Note: An orb of discord cannot be placed on someone behind a shield, so if you stay behind one, you won't have to worry about getting one.
Also, as @uni and @yuuki mentioned, some abilities can remove the orb from you.
Solution 3:
Tracer's Recall ability removes Zenyatta's Orb of Discord and, technically, Mei's Ice Wall can remove it by breaking line-of-sight. Reaper's Wraith Form will also remove Orb of Discord.