The God of War series are probably the most prominent games to feature QTEs and probably the reason for their prominence in more and more high-profile games. As seems to be the consensus among gamers (especially those who consider themselves more hardcore) I hate quick time events. I think they tend toward lazy design and generally don't add anything to a game. In seemingly direct contrast to that I am a huge fan of the God of War series.
So why do I love the God of War series in spite of heavy QTE usage? The obvious answer is GoW's implementation of QTEs. GoW, by its nature, is a very punishing game. I've seen people try and lump it in as a button masher, but that's not an overly accurate thing to say about it. You can get by to some extent by just mashing buttons, but once you really get into the games (assuming you don't play on the easiest difficulty) you need to learn the various combos and moves. You will need to utilize the various spells and above all you need to stay on your toes. Dodge and block are huge assets because the games simply don't forgive sloppy button mashing fighting. Just as you can attempt to claim a game such as Street Fighter 4 can be played with button mashing (which it can), people with knowledge of combos and movesets excel over even the most talented of button mashers.
The series gets a lot of shit from people for the QTEs, but I don't think that's entirely justified. While the games do use them during some cutscenes, the majority of them are used during battle. For example if you beat up a larger enemy long enough a circle button icon will appear above their heads. If you then walk over to this enemy and press that button (circle is the grab button) you enter a short quick time event where you press three or four buttons in sequence in order to quickly dispatch of said enemy. If you fail the sequence the enemy usually hits you for a small health loss. The main thing worth noting is these sequences are simply finishing moves, not a required part of the combat. You could simply keep whaling on the troll or cyclops and eventually kill them, but taking advantage of the finishing move saves time and potentially health and also usually nets you a larger powerup bonus upon their demise.
Another game I'm a big fan of, No More Heroes, also utilizes quick time events during combat. While you're fighting a button may flash up on the screen which allows you to finish off someone either by chopping them in half or performing a wrestling move. This is generally the best way to use QTEs if you absolutely have to, because it amounts to an extension of gameplay and does add some degree of challenge. I also suspect it's easier than designing a standard control scheme for suplexing someone. The major selling point is that these types of events are optional but very satisfying to pull off.
There are other, non-optional QTEs in the GoW games. For example while fighting one of the games many bosses often you will be required to execute a quick button sequence to unleash more damage. These are the ones I have more of a problem with, though the series tends to at least make them satisfying to watch and they are generally extensions of the in-game camera so you never feel torn out of the game.
Cutscene QTEs are the crux of the problem with QTEs. The majority of them tend to reolve around adding interaction to a traditionally non-interactive portion of video games. I'll use Resident Evil 5 as an example. The game plays out like a fairly normal action game; that is you shoot a bunch of dudes and collect items. After playing through enough of the game you end up in the old storytelling standby, the cutscene. Normally cutscenes are used to bridge the gap between levels. You find out something and because of this new fact you need to jet off to some totally unrelated place. Speaking in video game terms it's what happens between the lava level to the ice level. However along with these types of cutscenes, RE5 features a number of action-oriented cutscenes. The first one you encounter involves you and Shiva being attacked by a group of zombies on motorcycles (this isn't an RE5 review, so don't even get me started). You're totally surrounded by them and the scene plays out like something from an over- choeroegraphed action movie. One of the zombies takes a ramp and flies towards our heroes with a chain swinging above his head. Suddenly the scene slows down and the chain comes swinging towards you and your loyal companion. A blue X button graphic appears on the screen. If you press it you are treated to more of the cutscene followed by more QTEs. If you miss it you instantly die and have to start over.
While this mechanic isn't entirely horrible on its own (though it's pretty close) there's absolutely no lead up or hints that it's suddenly going to occur. Years of gaming have entrenched into my mind the belief that I can just sit back and watch a cutscene. RE5 has no prior focus on QTEs until to this moment. Literally you've been playing the game for probably 30 or 40 minutes at this point when suddenly a big 'X' pops up on the screen during a portion of the game where you traditionally don't have to worry about being killed. I believe I am more forgiving when God of War uses this mechanic because QTEs are a pretty big part of that series and you are presented with them almost from the beginning of each game. Furthermore, whenever you enter a cutscene QTE in GoW it's always lead up to by a normal non-interactive cutscene. Kratos never has to dodge attacks in the middle of a conversation. It's a fairly small difference, and some may not even see it as a difference at all, but I believe it's a fairly important one.
So what's the proposed solution to all of this? I'm not a game designer by any stretch, so take this as you will. First off I would say don't bother with them. If you have a highly choreographed action scene in mind that is impossible for the player to actually play, either don't put it in your game or don't make it fueled by a mediocre Guitar Hero session out of nowhere. Why do I need to be in this scene where motorcycle zombies jump over me and try to kill me with chains? Why can't I actually play it? Perhaps consider letting me shoot the zombies as I've done for the entire game prior to this moment. Though that issue is actually delving into a major part of the problem with Resident Evil 5 which attempts to be both a Resident Evil horror game as well as an action game where things like concurrent movement and shooting are necessary. The RE4 combat mechanics simply don't allow you to have interactions with anything that can move too quickly, although the game certainly tries it on numerous occasions with varying degrees of success.
In the end cutscene quick time events mostly just come across as insulting. They seem to be an attempt to bridge the gap between gameplay and a non-interactive cutscene, but only succeed at being an annoyance. When they simply amount to "press X to not die" (to quote Ben Croshaw) they don't really add that much to a cutscene except that now maybe you'll have to watch it two or three times because you accidentally hit the wrong button. While I tend to think that video game storytelling needs to evolve past the combination of cutscene, gameplay, cutscene, gameplay, I don't think adding random timed button presses to some of the cutscenes is the way to accomplish this. Video games, especially action games, have one advantage in terms of storytelling that no other storytelling medium has, which is that the person experiencing the story is actively participating in it rather than just being an outside observer.
(Readers who have not played BioShock may want to skip this next paragraph to avoid spoilers.)
Games like the Half-Life series and BioShock are excellent examples. Never pull the player out of his own viewpoint, and only let him know what people in the world think he should know. BioShock in particular was even a commentary on how video games amount to players following a set of instructions. When it seems like you have a choice, you are actually just doing someone's bidding. You're following a set of instructions. You're a slave to the world, and it's actually entirely out of your control. BioShock itself never offered up a solution to this problem, but in the moments when you finally face Andrew Ryan the game finally tears control away from you as you watch yourself brutally kill a man who refused to compromise. After everything you've wrought upon Rapture and its doomed citizens, somehow this single death has more impact than everything combined. Now imagine the game telling you to press the Y button to swing the golf club. Now press X to hit him again. Quickly press down to hit him one more time. How much impact would that have? How much would you really be in control?