Ironically, I am probably the least-equipped of our AMers to answer this question...because I've probably learned more about how human memory works than other AMers. So I'm not sure how to answer the question as posed, because my mind is buzzing with all sorts of follow-up questions (Do you mean semantic or episodic memories? Are you referring to encoding or retrieval? And so forth...)
But, if I set all of that aside for a moment, it does occur to me that I wish I had a better memory for proper names.
Often, I can think of a person, a place, a book, a movie, etc. and I can remember details about the subject, but I can't remember a proper name ("You know, it was the movie where the poor guy on the ship fallls in love with the rich young woman..."). Being able to recall proper names would often make my conversations flow more smoothly.
FWIW, that mostly qualifies as an aspect of long-term memory.
