Case reports still serve a valuable role in today's literature, but not nearly as significant as they once were. Some people love writing up case reports, and consider it a hobby. One can argue as to whether publishing a case report constitutes research at all. Regardless, they certainly are not "easy" to get published.
Many people make the mistake of finding a "cool case" and then trying to squeeze a report out of it. If it isn't truly unique, then the reviewers won't care about it, and it won't get published, so don't waste your time on a weak case. Remember, you have to go through real peer-review for a case-report, which can be arduous at times. A well-crafted case report is not an easy thing to construct, balancing the case presentation with a historic perspective and prior literature review, so make sure you have a good mentor as a last author to help you along the way. A well-written but unsurprising case is more likely to get published than a very unusual but poorly presented one.
Personally, I did a few in medical school, but since getting into funded research, I don't bother anymore. They don't count toward your career advancement in the clinician-scientist track.
