The Bench Dip is a very common exercise in many workout routines. Because you can use a park bench, an aerobic step, a short wall or even a chair, it's a staple in many group fitness classes as well as bodyweight and bootcamp programs.
There are also ways to make it harder or easier depending on the participant's fitness level.
We used to do it with our hands on one bench and our feet on another; the guys did it with a 45 pound plate on their legs.
Up until 3 or 4 years ago, I still had some clients doing Bench Dips but I don't anymore. I'm sure that some people could do them occasionally with no ill effects but why take the risk? When the guy called "the smartest man in fitness" by many other fitness pros talks, I listen. I even named my blog based on a post he wrote. You can read it here.
Anyway, regarding this exercise, Bill Hartman says:
The bench dip requires about 90 degrees of shoulder extension which exceeds normal shoulder extension by about 25 degrees.
To achieve that much range of motion the scapula must tilt forward which is a pretty unstable position. This also means that the shoulder joint is unstable and increases demands on the rotator cuff especially the subscapularis.
Over time this is a lot of undesirable stress leading to impingement of the cuff. This doesn't even consider the stress on the AC joint. It's also a crap exercise for overload.
Try Parallel Dips or Close Grip Pushups instead of Bench Dips.