All instructors working under the auspices of a training agency - regardless of that agency - are required to abide by minimum training standards. If an instructor could be demonstrably proven to have not met those minimum requirements, and yet still certified the diver, then for sure there is room for liability and litigation. Proving that, on the other hand, might be quite complicated without qualified, independent witnesses.
Once you are certified, as posted above, you are responsible for yourself, same as having passed your car driving license. The bulk of my work these days is actually guiding, not teaching, and therefore I often deal with the fallout from incompetently-trained divers. Sometimes, when I question them I get a response such as "my instructor didn't tell me that, we didn't have to do that, it wasn't part of the training" or something similar, and all I can do is try to fix the problem. I wasn't there, I wasn't involved in the training, and perhaps the student simply forgot that they did a particular task or skill, so I can't automatically state that the instructor was at fault. Perhaps the diver was great during training but without their buddy or instructor in the water, don't feel so comfortable any more - it happens.
Some of my colleagues see it as black and white: We are nothing more than underwater tour guides. We give a briefing and as long as divers keep to the briefing, we have no responsibility towards them beyond that. If they choose to ignore safety advice or deviate from the dive plan, then they are on their own. Me personally, I see it as a huge grey area and feel that actually, I am indeed responsible for all divers at all times, from the moment they get onto the boat until they get back to the bar at the end of the day, and partly this is because sooooo many divers believe that we are, indeed, there to look after them.
A case I always like to quote was one printed in PADI's Undersea Journal a few years ago. Two very overweight divers, a husband and wife, participated in a group dive and the husband sadly had a heart attack and passed away. The family tried to sue the dive operation firstly, because they didn't have a crane on the boat to lift the guy out of the water, and when this failed, they tried to sue the DM because he should have prevented them from entering the water, knowing they were unfit to dive. Both lawsuits thankfully failed, but in a sense, the final outcome doesn't matter - somebody still got dragged through the courts and that must have inevitably been a terrible process, given the litigious climate we live in these days.
As an instructor, you have agency standards to follow and if you break them, even in a small way, then you automatically lose your agency backing. As a dive guide, the rules that apply are those that are stipulated by international/local law and regulations, such as with regard to maximum depths and suchlike. As an example, local law in Egypt says that the maximum depth for a single tank air dive is 40m (with appropriate experience or training) so if I took somebody to 50m and they had a serious problem, then for sure I am going to jail, but I cannot be sued because PADI (For example) recommends a maximum depth of 30m for Advanced Open water divers.
As for cases - I would have to leave that open to others... I tend not to read about them, they give me the shivers!
Cheers
C.