I'll add a coupla more in the "other" category.
One thing that makes an item interesting to me is history, that is a personal connection to the item as a matter of family history. I have had a number of personal artefacts handed down to me by my father, grandfathers, great grandfathers. A drafting table and machine (which I still use), an engineering slide rule (which I rarely use but have hung in my bedroom and taught my children to use), old pocket watches, guns, a bayonet taken form a dead Japanese soldier won by my uncle in the Pacific, ration cards form World War II, various historical documents, a rosary, binoculars and telescopes, compasses, surveying equipment, tools, a fedora, even old fishing equipment and tools, etc. They are all interesting, some even fascinating, because of their historical background to my family.
In game terms I can imagine a number of fascinating artefcats also passed down through family lineage and inheritance that might have some secret or hidden magical property, or to which one could attach a magical property in order to match the sympathetic and historical value of the object. But "passing down things" was a common historical practice that was engaged in many cultures. I can't imagine it wouldn't also be a more or less common practice in any fantasy worlds but far too often the game seems to start every one off as if they are "a recent graduate" fresh to the world with just a credit card to their name to buy all new equipment to tackle the world. And as if the only member of the character's family to have ever add nay kind of spirit of adventure is the player character himself. It's hard for me to imagine every adventurer being an outcast from his family's history and historical tendencies, as if he or she alone were the only "adventurer" of any kind in the entire history of their family.
History though, personal and family history, that adds a real dimension of great depth to a thing. Heirlooms should be far more common it seems to me than they are in most fantasy games. And it is a fascinating aspect to explore for possible adventure ideas. For instance...
1. Discover the real history of an item
2. Discover if it is magical
3. why does your family possess it? For what purpose?
4. Can it become magical?
5. Is it one part of a larger item?
6. Is somebody else looking for it or do they want it back?
7. Where was the item originally located?
8. Who made the item and why?
9. Is the item famous in some circles?
10. Is the item secretly cursed or blessed?
And so forth and so on...
Another thing I have been recently experimenting with is magical items that change over time. Develop new capabilities and functions, perhaps lose old capabilities and functions. I'm even experimenting with one item that actually changes shape over time and becomes something other than what it appeared to be at first.