Sometimes I'll have a question that I know I asked before, maybe years ago, and got a good answer to, and need to refer back to. I could probably eventually find it using the relevant site's main search, but it would be a lot faster to be able to just search within my profile through the couple hundred questions I've asked before. It would also be nice to be able to filter them by tags.
Same with answers and favorites, now that I think of it.
Edit: I did see this question, but that's 6 years old and I'm not convinced it's the ideal way of implementing this. I don't see why I should have to type my own username....seems to me it would be a lot more intuitive to be able to just go to my profile and type in a searchbox right there. The third-to-top answer on that question is actually hilarious in terms of the amount of effort required. Recommended reading.