Why does sauron need the one ring?

Sauron needs the one ring because it is his life. He and the ring are bound to one another. Sauron really did die, but since the ring was not destroyed his spirit remained in Middle Earth. If the ring was destroyed, then Sauron would finally die.

---

It's really a very simple answer:

Sauron is made up of a life force, which before the ring was made, put him at 100% life force. He then decided "Hey, I can put some of this life force into a ring, and then twist it so that I have awesome super powers." So he did. Before you know it, he's going house on people and teaching them what's what.

Then Isildur grabbed up the sWord of his fallen father, Narsil, and was like "Not on my watch" and wrecked him, taking the ring for himself. Sauron was basically like "oh crap" because like 99% of his life essence just got taken away from him and he basically only has enough to command his troops and manifest as a fiery eye. Even that, however, is tenuous, for it is only doable because out there, somewhere, the rest of his life essence lives on in the form of this super-powered ring.

So, if that ring is destroyed, he loses the ability to manifest at all. Thus being destroyed.