Let's look at the list, shall we (for fairness, I've treated young only items and adult only items at age value instead of whole-game value):
Kokiri Sword - Very useful, but very weak. Almost never necessary.
Deku Shield - Very useful, but burns up easily. Almost never necessary.
Slingshot - Very useful and quite often necessary.
Bombs - Very useful and quite often necessary. Chance to self-damage.
Boomerang - Very useful and quite often necessary.
Master Sword - Very useful but never necessary other than story-wise.
Bow and Arrow - Very useful and quite often necessary.
Megaton Hammer - Slow weapon. Not very necessary, but much more useful than given credit for (revealing holes in walls, glitches, easier battles, etc.).
Hookshot - Very useful and quite often necessary. (Downgraded Longshot)
Longshot - Very useful and quite often necessary. (Upgraded Hookshot)
Lens of Truth - Awesome and interesting item, very helpful at multiple points but never absolutely necessary.
Hover Boots - Awesome, but late game and only somewhat necessary.
Mirror Shield - Awesome, but late game and only somewhat necessary.
Iron Boots - Slow, but necessary for certain things and more useful than given credit for (less knockback, no accidental running, etc.),
Epona - Helpful, sometimes. Often slows me down more than speeds me up.
Biggron's Sword - Helpful, but not useful in a way that isn't new and never necessary.
Bottles - Super useful, but only necessary for the blue fire.
Ocarina of Time - Only necessary for story aspect. Scripting shows the Fairy Ocarina will work for all of the songs.
My favorite on that list is the Megaton Hammer, and thus it gets my vote.
Though, the question is "Which do you need the most?", and, all things considered, either the Bow and Arrow or the Hookshot/Longshot is the single item with the most necessities in the game, though almost all of the items are necessary at some point, either story or play related.
(If the HS/LS are considered one, then that wins it. If they are considered seperate, then the Bow and Arrow gets the single most necessities.)