For example a profile link in an app could read "your profile", "my profile" or just "profile". Dusting Curtis talks about the distinction between using "you" or "me" in his article Yours vs. mine, but I think the discussion needs to consider the third option of just omitting the pronoun. Digging deeper, the issue isn't even that simple. You could also use the users name in place of a pronoun, like Netflix does.

I usually prefer omitting the pronoun, especially in the case of labeling folders or views that contain the users files. For example in Windows XP every possible folder containing user files was named "My something". I never felt any of those pre labelled folders were actually mine despite the name, since I didn't create them, even though I might name my folders exactly that if I created them myself. I once made an "Omat tiedostot" folder on my desktop, which is Finnish for "My documents" and only realized a few months later that yeah, that's the same thing. I like to let the user name their things with "My" naming if they want, so they'll feel ownership, but I won't create those for them.

If a conversational tone is needed, I prefer "You" as the pronoun, as if the app is talking to the user. It's also what other people would say to the user if they saw their stuff. Because interfaces are not only labels and buttons, It may sometimes be necessary to choose a pronoun and stick to it. For longer passages of text, "you" is often the most natural term to use. In my experience, most often the perspective there is as if the used had asked a question and the interface was answering it. Like "How do I accept a transaction" and the UI would read "You must click the accept transaction button". Some apps mimic being a person and will talk to the user directly, saying things like "Just a second, I'm still searching".

Of course the choice always depends on target audience, brand and other circumstances. There are good discussions on the topic at Layervault and UX Stack Exchange, with links to even more articles. Here's some further reading:

After reading these, it would seem to me that experienced computer users, who have a good understanding of how to navigate interfaces, are comfortable with UI labels without any pronoun. Less experienced users on may need more of a sort of hand holding, or comfort, by having "my" or "your" in labels, depending on the context.

Whether you label things with "your" or "my" relates more to the overall user experience and feeling of your app, than directly to usability. From a usability perspective, consistency is the important thing. If you have something like "Find your My Photos" in a help screen, things may get confusing pretty fast. On the flip side of this is how your app or brand refers to itself. That's another topic entirely, but for copywriting geeks and other smart people, Mailchimps Voice and Tone is a great place to start thinking about it.