When done right QTEs make the gaming experience so much better. A good example of this is the Leon and Krauser knife fight in Resident Evil 4.
Really? I hated that one. I don't think it's a good idea to convey important story elements while forcing your player to be on edge and having them press buttons asap.
That's why I loved it so much. I usually have pretty quick fingers and I'm pretty good at hitting QTEs without warning. However with this one, I was so into the story that I missed it a couple times my first run through. The fact that I'm trying to listen and understand what's happening while preparing for the inevitable prompt to dodge, makes the moment all the more intense.
From a pure, story conveying perspective, it probably wasn't the best time for QTEs but it did help portray Krauser's personality quite well.