As far as required items go, it's a toss-up between the Dominion Rod and the Spinner. Both are barely used outside of their respective dungeons, but the Spinner is used to get some heart pieces and for one spot in the Temple of Time and Hyrule Castle. The Dominion Rod, on the other hand, has an entire questline surrounding it. So it's difficult.
The Ball & Chain is far from useless. It works incredibly against ReDeads and Skulltulas, and is fantastic in the room in the Cave of Ordeals with freezards and chillfos.
However, I think the most useless item overall is Bomblings. They are not required, and to be honest, there is no reason to ever buy them from Barnes. You have far less control than you do with regular bombs and they are so expensive. The only place in the entire game where they are useful is in the Forest Temple, where they're just enemies and not even an item. In no scenario would I ever choose to use Bomblings over regular bombs.