So many times. I can't even count them,countless Abra alone..also numerous that managed to break free of the Quick Balls..Those are the only times I can see False Swipe actually working..Sawk comes to mind,Aipom too,Swanna,a few Wurmples and some others early on also Tyrogue also I remember trying to catch a level 6 Riolu in X and it literally took forever and it took a ton of different kind of balls even though my Pokemon was very high leveled at that time and I'm pretty sure my Pokemon had hypnosis as well..I'd figure level differential would make a difference(especially with even trying a nest ball and that didn't even work)...evidently not and it can get frustrating too>.>

I was about to say no, but when I saw Abra... I changed my answer.

I agree with MCHopnPop about the move False Swipe coming in handy at those moments. (Of course, I am glad that, in Pokémon FireRed and LeafGreen, the Pokémon Abra can be bought at the Celedon Game Corner for 120 Coins, which would save me some time in trying to catch it in the usual way.)