Specifically:
- The weapons from primal hard modes (Ifrit, Garuda, Mog, etc.)
- The Odin/Behemoth rewards
- i90 Mythology Gear
- Possibly CT gear, although it's only really because of the Warrior of Light set
- Possibly even the lvl 1 crafted outfits, like the glacial coat and spring dress
There's way too many great novelty items that upon getting, I can't really force myself to part with although I might never use them (besides maybe the occasional glamour). Some of them are pretty unique just by how rare it is, like Zantetsuken and Thundercloud, and barely even have any other use outside from looks.
Admittedly, I am definitely a hoarder anyway in these kinds of things. I'm still holding on to the lvl 15 and 32 dungeon pieces because I love the way they look, and there was a lot of effort involved. Honestly not everything should be permanently stored, I can't believe an MMO has a feature like this to begin with, but I know I'm not the only one with inventory problems still.