I don't know if this is best but
WWE 2K14
I kind of like how it did quick times for the "WrestleMania Moments." Basically, in the single player portion of the game, you're playing through a history of wrestlemania, and most of the match you control the wrestler who wins the match (historically) and you basically just beat down and wear your opponent, but there are some circumstances where the game "takes over" to re-enact a famous moment in WrestleMania. Some reviewers didn't like this because it really takes the control out of your hands and into a scripted sequence of quick time button presses... But, hear me out, wrestling is a staged athletic theatre, and, really, if you want to recreate a "Hogan No Sell" or what have you, then you have to take power away from the player to recreate that moment.
They also use it well in the Royal Rumble, where when eliminating a guy near the ropes, you have to follow a handful of button presses... You initiate this litle contest and depending on how worn down your opponent is or how worn down you are, it requires me precise presses.
Also, when getting pinned. When you're pinned, a meter comes up and you have to press "A" at the exact moment in the middle of a moving bar... This isn't entirely a quick time but it's similar, really needs to be timed well, and it's much better than the old fashioned "MASH EVERY BUTTON AS FAST AS POSSIBLE" because it does allow for some kick outs when you really shouldn't be able to kick out.
Maybe not the best, but memorable for me.