Note: They did not pick their "Divorce" or Ted and Robin's breakup because who cares about that right?
They choose their first breakup! :D :(
When their friends noticed that Robin and Barney were going through a rough patch, they plotted to break them up. When they did break up, Barney was devastated and felt they couldn't go back to being friends.
http://www.answers.com/article/1182862/10-truly-heartbreaking-tv-breakups?param4=znt#slide=3