For me, it was during a game of 
support, our allied 
had just turret dove and was about to die, and in addition to not ulting him in time, I also accidentaly ulted myself just after he died since we were close together.
Threw a Malphite Q for the finishing blow and walked away while flashing mastery, only to realize I Q'd a minion.
Not a single fail but a chain of fails : Missed hook,missed flash flay and ult that didn't hit anyone.
But my exhaust did hit so I got that going for me which is nice. 
My largest fail was trusting my teammates.
Whenever I manage to miss a point and click ability like Malphite's Q or Karma's W.
Then I know its time to take a break.
Forever.
if champion select counts then - forgetting smite and creating a new mastery page just to not have time to save it.
in game it's probably when i mistook mia ping spamming for actual mias and ran back to the turret causing me to miss a kill.
If you play Orianna... You find a new fail every week. and It usually always involving missing an ult.
I love him but the learning curve for 
was unkind.
The times I missed my f***ing smite onto the goddamn mini wraiths when you could smite the sonsabitches.
I felt retarded every time.
getting permabanned fro going off on my adc who went off on me after gettign him a triple kill then he stating to me to not fucking feed you stupid useless noob supp
