I won't include the swords in this since that's kind of a necessity in any situation. I think it's implied that you couldn't do without the swords. I'm torn between three items... those three being the Deku Nuts, Mirror Shield/Hylian Shield, and Bow and Arrow. Sadly, the Deku Nuts aren't a poll choice. Let me explain why-
Deku Nuts are extremely convenient and strategic items. People don't give the Deku Nuts as much credit as they deserve. People view them as something secondary that you don't really have to use, and you don't, but it makes your life a lot easier if you know how to utilize them well. I think that the Deku Nuts are on the same level as Farore's Wind. There are some great and helpful ways to put it to use, but people simply don't utilize them. The Deku Nuts can be life-savers in many situations. I'm just going to come right out and say Jabu-Jabu's Belly with the jellyfish. That's probably where the Deku Nuts would come in handy the most out of anything.
I can think of a few more scenarios off the top of my head, too. Imagine you were playing Master Quest, and there was this pesky Deku Scrub that you needed your Deku Shield for in order to deflect its attack. Well... next imagine there are a few Fire Keese flying around in the room. This doesn't sound like a pleasurable scenario, does it? On one hand, you want to unequip the Deku Shield so it doesn't get burned, but on the other you
need the Deku Shield to defeat and protect yourself from the Deku Scrub. Solution: throw down a single Deku Nut. It will stun all of the Fire Keese nearby, putting the flames out and leaving them wide open to attack. This kind of situation, or any situation with Keese, fire or not, for that matter, would be a perfect one to use Deku Nuts in. It can also be used to stun a variety of different enemies, as well, making them all the easier for the picking.
Then we have the Mirror Shield/Hylian Shield. I guess the Deku Shield would sort of fall into the category, too. I just need a shield for my everyday butt-kicking, ya know? I mean, what do you expect me to do? Walk into the Forest Temple and fight a million Stalfos at once without any shield? Are you nuts? Well, I guess if you're doing a minimalist run then you may do that, but I still think you're crazy if you're not using a shield. It may not be absolutely mandatory for a lot of battles, but it certainly takes a load off your mind and helps you relax. Not to mention those moments where it is just an absolute life-saver. What would we do without swords, shields, and magic?
Then we've got the good ole Bow and Arrow, probably my favorite equippable item in the entire Zelda series. I've put the Bow and Arrow to a great many uses, and Ocarina of Time is no exception to that. I've used the bow and arrow when I just get tired of hacking away at things. I do admit that the Bow and Arrow saw a lot less freedom to be used in Ocarina of Time than a game like, say, Twilight Princess, but it was still great to utilize from time to time. You could take out those pesky Keese, shoot some floating skulls through the empty eyesockets, or just be a coward and pick away at enemies from a distance. [noparse]
[/noparse] It was also really fun to shoot the Gerudo while infiltrating the fortress with the Bow, too.