We just finished work on an extensive 2 year renovation of the New Course at Himmerland Golf Club in Denmark. They had/have a par 6 (now hole 11) which they were keen to keep. It is a relatively challenging type of hole to design, as the length alone exhibits the difference among golfers in terms of carry/length. For some it is easily reached in 3, while other will struggle to be on the green with 5 or 6 good shots. A lot of golfers will feel it creates a lot of 'transportation-type' golf shots, which are generally not as interesting to play. I believe these are the main reasons why we don't see more par 6 holes around. It measures approx. 610m (680yds) into the prevailing wind.
As Tom Doak mentions, it does connect hole 10 and 12 better than having a par 5. The club is trying to bring the European Tour back to Denmark for the first time in more than 10 years - but we have advised them to play it as a par 5 (perhaps from a slightly forward tee).
I personally found it a bit gimmicky in the beginning, but it has grown on me during the project, and it is actually a very different and fun golfing experience that (if designed properly) creates a challenging and memorable golf hole.