In what situations would it be appropriate to include one's photograph in a CV?

In the United States, you should never include a photo in an academic CV. It comes across as somewhat inappropriate, like you are deliberately drawing attention to your appearance and hoping it will influence the decision. (I know that's not actually the intent, but many people's gut reaction upon seeing the photo will be "Why is the applicant showing me this? Do they think I should know what they look like before making a decision? How is that supposed to be relevant?") If you are from a country in which photos are often included, then that will be understood as a reasonable explanation, but it will stand out as foreign. If you aren't from such a country, then it will look bad.

If you apply for a job or for grad school in Germany, a photo will be more than appropriate (unless there are other rules or specific forms for the position or school). Indeed it is quite the norm to have a photo on your CV for job applications in Germany (both inside and outside academia). However, if you have a CV attached to, e.g., a grant proposal, then a photo would look strange.

First, there is no clear cut right or wrong here and the short answer as I see it is that there is no question of appropriateness, but maybe of impact.

I see quite a few CVs at different stages in academia and the majority lack photos but a fair number carry them. From my perspective, I would say that persons in or aiming for academic education are the ones that to a larger extent add photos to their CVs. People applying for higher academic jobs, after their PhDs, do it less. The latter is likely due to the fact that when applying for such a job it is the merits (publications, teaching experience etc.) and the experience in research which receives all focus. An image is irrelevant.

So why will (mainly) younger persons add photographs? I agree that tradition (e.g. in different countries) plays a role. I can also imagine that it may seem like a good way to present themselves amongst a more anonymous mass. Whether or not this is successful, I am not certain. But, it is true that these applications stick out and are noticed and for good reasons. As social beings we are used to see faces and communicate with persons so an image may have an effect. Unfortunately, due to irrelevant reasons but hopefully in very few instances, some people may also let the picture influence their views of applicants that overshadow the official selection criteria but that is another story.

To add to the picture, most people have personal web pages of a facebook page with images of oneself and other things related to life and activities. A link to such pages (e.g. through a QR patch) could be more efficient to relate personal traits and interests than a photograph in a CV. This does not mean that all will take the time to see the pages.

So for any academic use, I do not see an image as important. Use of a link to social media incl. web pages may suffice, if one thinks there is something valuable to see there. So the appropriateness is not an issue as I see it but the positive effect, if any, may decrease with time since important assessment criteria are progressively filled with information.