I'm one of the many people out there that have really enjoyed these films and the third installment might even be the most action-packed of the series thus far.
The stories in these films are intertwined, but to be honest, you won't really be that confused if you don't see the first 2 before watching 3. I would imagine that such knowledge enhances the experience but it isn't essential to it. I think that I enjoyed John Wick 1 the most out of the bunch because John was a mystery to everyone and the story had yet to become something that involved an international group of assassins - which is the road that it has gone down extremely in part 3.
This story begins less than an hour after John Wick 2 ended and John has been declared excommunicado, meaning that he no longer has protected status inside the organization that he works (ed) in and has now become hunted, and there is a bounty on his head for anyone that finishes the deal.
Thus begins a very high-paced and nearly break-less sequences of fights and events. The action comes at us pretty non stop and the fight sequences are pretty inventive, which is what this series has become known for. Of course, there are also a ton of deaths, which is likely the other things they are going for.
I wouldn't say this movie was particularly amazing for any reason other than it is a good action film and stays exciting the entire way through. They are kind of losing me with the story of the far-reaching assassin organization called the "High Table" and it think it is pretty obvious that John Wick 4 is going to be about Reeves feeling compelled to destroy them next. However, the fight scenes are fantastic, Reeves is perfect for his role and it is always nice to involve Ian McShane is just about anything even though his role is relatively minor.
Overall, for action and wonderfully-choreographed fight-scene fans, this is a must see. Just don't expect a story that is really going to make you think.